UC-NRLF 


SWITCH  WO. 


REESE  LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


^Accession  No.     /  0  *7  /  j   •    Cla& 


ss  No. 


Entered  according  to  Act  of  Congress,  in  the  year  1891, 

BY  D.  H.  I.OVKI*!*, 
In  the  office  of  the  librarian  of  Congress,  at  Washington 


INDEX. 

PAGE 

The  Turnout 7 

The  Theoretical  Lead 10 

The  Shortened  or  Practical  Lead    . 14 

Turnouts  from  Curves •       21 

The  Stub  Lead 29 

Switch  or  Moving  Rails .       ..'...  33 

The  Frog  Number 36 

The  Frog  Angle -.  40 

The  Frog  Point    .    v  ,    .  >.    -. 43 

V    \      N.  \ 

A  Frog-Board 45 

Numbers  to  Use,  and  Where 48 

The  Gauge  at  the  Frog 51 

Widening  the  Gauge  of  Curves .  53 

To  Line  Turnout  Curves 59 

The  Line  at  the  Heel  of  the  Frog 67 

Cross-overs  upon  Straight  Line 70 

Cross-overs  upon  Curves 84 

Three-throw  Switches 89 

A  Ladder  Track 100 

Switch  Timber in 

Curves 127 

A  Regular  Curve 127 

A  Compound  Curve ,   .  128 

13) 


4  INDEX. 

PAGE 

A  Reverse  Curve 129 

The  Degree  of  Curvature 130 

To  Ascertain  the  Degree  of  Curvature 133 

The  Limit  of  Curvature       ..'... J38 

To  Line  a  Curve 139 

The  Elevation  of  Curves 148 

The  Approach  of  Curves 161 

To  Line  and  Elevate  a  Reverse  Curve 172 


UNIVERSITY 
PALIFO 


PREFACE. 

THERE  is,  perhaps,  no  part  of -track  work  in 
regard  to  which  there  are  so  many  unimportant 
differences  of  opinion  upon  the  part  of  trackmen 
as  that  which  pertains  to  switch  work.  Track- 
men naturally  form  their  opinions  from  local  con- 
ditions, and  follow  the  practices  of  their  prede- 
cessors or  the  instructions  of  their  superiors,  so 
it  would  be  only  natural  for  each  one  to  think 
that  his  way  is  the  best. 

This  book  is  intended  for  the  trackman  par- 
ticularly, to  give  him,  in  a  concise  and  compre- 
hensive way,  what  is  the  best  general  track  prac- 
tice, from  which  he  may  select  that  which  will 
best  meet  the  requirements  or  conditions  under 
which  he  may  work. 

There  are,  of  necessity,  in  a  book  of  this  kind 
slight  but  unimportant  departures  from  mathe- 
matical accuracy,  also  what  may  seem  unneces- 
sary detail  of  explanation,  and  also  the  use  and 
frequent  repetition  of  words  or  expressions  which 
are  common  among  trackmen,  all  of  which  are 
necessary  to  make  it  thoroughly  understood  and 
useful  to  this  most  worthy  class  of  practical  men. 
(5) 


O  PREFACE. 

It  is  not  expected  that  the  formulas  will  be 
intelligible  to  them,  but,  so  far  as  possible,  where 
it  is  necessary,  the  formula  is  accompanied  by  a 
simple  mathematical  demonstration,  which,  it  is 
hoped,  will  not  be  beyond  the  clear  understand- 
ing of  all. 

It  is  nqt  claimed  that  this  is  something  new 
and  superior  to  anything  hitherto  published. 

It  is  simply  a  combination  of  theory  and  prac- 
tice, so  far  as  possible,  based  upon  common  sense 
in  track  work  and  verified  in  the  experience  of 
hundreds  of  the  best  trackmen  of  the  day.  So 
there  need  be  no  hesitation  to  use  what  is  in 
the  book  from  a  fear  that  it  may  not  be  correct, 
should  it  happen  not  to  be  in  strict  accord  with 
local  practices. 


THE  TURNOUT. 

The  single  turnout  from  one  track  to  another 
is  the  most  simple  of  all  switch  connections,  the 
more  complicated  ones  being  only  developments 
of  it,  and  what  is  true  of  it  is  also  true  of  them. 

The  turnout  curve,  from  a  theoretical  point 
of  view,  is  most  generally  assumed  to  be  a  sim- 
ple circular  arc  or  curve,  beginning  at  the  point 
of  the  switch  point  or  head-block,  as  C,  and 
ending  at  the  point  of  the  frog  B,  as  shown  in 
diagram  No.  I  : — 


No.  1. 

That  portion  of  the  turnout  between  the  head- 
block  and  the  frog  point,  as  A  to  B,  is  called  the 
lead,  and  its  length  for  a  point,  or  split  switch, 
as  it  is  most  generally  called,  is  the  distance 
from  the  point  of  the  turnout  curve  or,  in  this 
case,  the  head-block  of  the  split  switch,  to  the 
point  of  the  frog  measured  along  the  main  or 
straight  rail,  as  A  to  B  in  diagram  No.  i ;  and 
for  a  stub  switch  it  is  the  distance  to  the  frog 
(7) 


8  PRACTICAL  SWITCH  WORK. 

point  from  the  head-block  only,  the  former  be- 
ing called  the  "point  lead"  and  the  latter  the 
"stub  lead." 

The  turnout  curve  is  from  C  to  B,  and  al- 
though the  difference  in  distance  between  it  and 
the  lead  from  A  to  B  is  only  a  few  inches,  it 
should  not  be  mistaken  for  the  lead,  nor  so  re- 
garded. 

Whether  the  turnout  is  from  a  straight  or 
curved  track,  or  the  switch  is  a  point  or  a  stub, 
the  lead  should  be  measured,  as  from  A  to  B, 
along  the  main  rail  in  which  the  frog  is  already 
or  is  to  be  placed. 

Before  any  lead  can  be  calculated  or  ascer- 
tained it  is  necessary  to  know  the  gauge  of  the 
track,  the  frog  number,  and,  in  the  case  of  a  stub 
switch,  the  throw  also,  as  the  lead  and  the  de- 
gree of  the  turnout  curve  vary  for  every  differ- 
ent frog,  throw,  and  gauge. 

Practically,  the  difference  of  a  half  inch  be- 
tween the  two  standard  gauges — 4  feet  8J  and 
4  feet  9  inches — is  so  small  that  there  need 
be  no  difference  between  them  recognized,  al- 
though it  is  well  to  do  so  where  the  distances  or 
rules  for  each  gauge  are  given  to  calculate  the 
lead. 

The  "throw"  is  the  distance  the  sliding  or 
moving  rails  move  at  the  head-block.  The 


THE   TURNOUT.  Q 

throw  of  a  point  switch  in  nowise  affects  the 
lead,  but  the  throw  of  a  stub  switch  does. 

It  has  been  found  in  practice  that  the  theo- 
retical length  of  the  lead  as  obtained  upon  the 
assumption  that  the  curve  begins  at  the  point 
of  the  switch  and  ends  at  the  point  of  the  frog,  is 
too  long  when  used  for  frogs  higher  than  No.  7, 
and  makes  the  turnout  curve  flat  near  the  switch 
or  sharp,  in  comparison,  near  the  frog.  This  is 
on  account  of  the  switch  point  not  being  thin 
enough  to  conform  to  the  theoretical  curve,  its 
gauge  line  at  the  heel  being  several  inches  in- 
side the  theoretical  curve  at  that  point. 

To  remedy  this  it  is  the  practice  to  reduce  the 
length  of  the  lead  so  as  to  obtain  a  more  uniform 
turnout  curve  between  the  heel  of  the  switch  and 
the  frog  point. 

To  distinguish  these  two  leads,  one  is  called 
the  "theoretical"  or  long  lead,  and  the  other 
the  "practical51  or  short  lead. 


THE  THEORETICAL  LEAD. 

As  has  been  mentioned  before,  the  theoretical 
lead  is  the  distance  to  the  frog  point  obtained  by 
calculation  upon  the  assumption  that  the  turn- 
out curve  begins  at  the  switch  point  and  ends  at 
the  frog  point. 

For  the  engineer,  the  formula  or  mathematics 
for  this  lead,  for  any  gauge  and  frog,  is  l  —  2gnt 
in  which  /  is  the  lead,  g  the  gauge,  and  ;/  the 
frog  number. 

For  the  trackman,  it  means  that  the  lead  is 
equal  to  twice  the  gauge  multiplied  by  the  frog 
number. 

For  example:  What  is  the  lead  of  a  No.  10 
frog,  4  feet  9  inch  gauge  ?  Twice  4  feet  9  inches 
is  equal  to  9  feet  6  inches,  or  9^  feet,  and  ten 
times  9^  feet  are  95  feet,  which  is  the  theoretical 
or  full  lead  of  a  No.  10  frog,  4  feet  9  inch  gauge. 

For  the  same  frog  and  4  feet  8^  inch  gauge, 
the  lead  is  twice  4  feet  8^  inches,  or  9  feet  5 
inches,  which,  multiplied  by  10,  equals  94  feet 
2  inches. 

For  No.  8  frog  and  4  feet  9  inch  gauge,  it  is  76 
feet ;  and  for  4  feet  8^  inch  gauge,  it  is  75  feet  4 
inches. 

(10) 


THE   THEORETICAL  LEAD.  1  I 

It  is  evident  from  this  that  the  one-half  inch 
difference  between  these  two  standard  gauges 
is  so  small  as  not  to  affect  the  lead  practically, 
and  it  is  not  necessary  to  make  any  distinction 
between  them  in  considering  and  applying  prac- 
tical rules.  But  for  the  purpose  of  making  this 
formula  and  rule  more  easily  remembered  and 
useful  to  the  trackman,  it  can  be  simplified  in 
this  way  : 

Rule,— For  4  feet  8|-  inch  and  4  feet  9  inch 
gauges,  the  theoretical  or  long  lead  is  equal,  prac- 
tically, to  9^  times  the  frog  number. 

9^  times  10  equals  95  feet,  the  lead  for  No.  10  frog. 
9^  times    8  equals  76  feet,        "  "         8    " 

9£  times   6  equals  57  feet,        "  "         6    " 

This  will  not  apply  to  any  other  than  4  feet 
8^  inch  and  4  feet  9  inch  gauges,  and  with  point 
or  split  switches.  For  all  other  gauges  use  the 
rule  of  "twice  the  gauge  multiplied  by  the  frog 
number"  for  the  theoretical  lead. 

The  following  is  a  table  of  leads  obtained  by 
this  rule  for  3  feet,  4  feet  S£,  and  4  feet  9  inch 
gauges  :— 


JP&ACT1CAL  SWITCH   WORK* 

TABLE  No.  i. 
THEORETICAL  LEADS. 


LEADS. 

FROG  No. 

4  Feet  8^ 

inches.   4  Feet  9  Inches.            3  Feet. 

Feet,    inches.       Fe"et.    inches,  i            Feet. 

4 

37 

8            38 

o                  24 

5 

47 

i             47 

6                  30 

6 

56 

6             57 

o                  36 

7 

65 

IT             66 

6                  42 

8 

75 

4             76 

o                 48 

9 
10 

84 
94 

9             85 
2             95 

6                  54 
o                 60 

ii 

103 

7           104 

o 

12 

U3 

o           114 

o 

15 

141 

3           142 

6 

The  use  of  this  table  is  very  simple.  Having 
decided  upon  the  number  of  the  frog  to  be  used 
in  the  turnout,  refer  to  the  table,  and  opposite 
the  frog  number  will  be  found  the  theoretical 
lead.  Place  the  frog  that  distance  from  the 
head-block  of  the  point  or  split  switch. 

If,  however,  a  shorter  lead  is  desired,  refer  to 
Table  No.  3,  on  page  16,  in  which  are  given 
shortened  leads,  which  may  be  used  instead. 

The  choice  between  the  theoretical  and  the 
shortened  lead  is  optional :  either  is  good 
enough,  but  the  shortened  one  will  give  a  bet- 
ter line  to  the  turnout  curve,  and  is  therefore 
preferable. 


THE   THEORETICAL  LEAD, 


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This  table  is  correct,  the  other  tables  giving 
only  approximate  figures. 


THE    SHORTENED,   OR   PRACTICAL, 
LEAD. 

The  practical  lead  differs  from  the  theoretical 
lead  in  being  shorter,  and  consequently  improves 
the  alignment  of  the  turnout  curve  for  frogs 
higher  in  number  than  seven. 

The  circumstances  to  be  considered  in  de- 
termining how  much  the  theoretical  lead  should 
be  shortened  are  :  the  clearance  necessary  at  the 
heel  of  the  switch  point  as  a  flangeway  for  the 
passing  wheel,  the  length  of  the  switch  point 
or  point  rails,  and  the  economical  use  of  ma- 
terial. 

The  clearance  between  the  gauge  line  of  the 
main  rail  and  the  outside  of  the  head  of  the 
switch  point  at  the  heel  should  not  be  less  than 
2^  nor  more  than  3^  inches,  '3  inches  being 
preferable. 

If  this  clearance  is  added  to  the  width  of  the 
rail  head,  which  is  about  2j  or  2|-  inches,  the 
distance,  gauge  to  gauge,  at  the  heel  of  the  switch 
point  would  be  about  5  or  5^  inches.  Assum- 
ing that  this  distance  corresponds  to  the  throw 
of  a  stub  switch,  the  stub  lead  can  be  calculated, 
giving  a  curve  from  the  frog  point  to  the  heel  of 
(14) 


THE  SHORTENED,    OR  PRACTICAL,   LEAD,          I  5 

the  switch  point  which  would  conform,  between 
those  points,  to  the  theoretical  curve  when  the 
lead  is  obtained  by  the  rule  of  "twice  the 
gauge,"  referred  to  on  the  preceding  pages.  And 
if  to  this  stub  lead,  so  obtained,  the  length  of  the 
switch  point  is  added,  provided  it  is  not  less 
than  15  nor  more  than  20  feet  long,  a  good 
shortened  lead  for  any  frog  can  be  obtained. 

When  any  switch  point  less  than  15  feet  is 
used  the  clearance  at  the  heel  should  be  reduced 
slightly,  otherwise  the  alignment  from  the  heel 
to  the  point  of  the  switch  rail  would  make  a  too 
abrupt  change  in  the  turnout  curve  at  that 
point. 

But  to  properly  secure  the  switch  point  at  the 
heel  with  splices,  the  clearance  should  not  be 
less  than  3  inches,  or  about  5|-  inches,  gauge  to 
gauge.  For  that  reason,  about  15  feet  is  the 
least  desirable  length  of  switch  point.  A  good 
rule  for  the  shortened  lead  is  as  follows:  For 
4  feet  S£  inch  and  4  feet  9  inch  gauges  the  lead 
for  all  frogs  up  to  and  including  a  No.  7  is  gj 
times  the  frog  number;  for  No.  8,9  times  the 
number;  for  Nos.  9  and  10,  SJ  times  the  num- 
ber; and  for  all  from  Nos.  10  to  15,  8  times  the 
number  of  the  frog. 

The  exceptions  to  this  rule  are  that  the  lead 
for  No.  9  may  be  78  feet  instead  of  76  feet  6 


i6 


PRACTICAL  SWITCH  WORK. 


inches,  and  for  No.  i  T,  90  feet  instead  of  88  feet. 
However,  those  obtained  by  the  rule  are  not  too 

-short. 

TABLE  No.  3. 

SHORTENED  LEADS. 


FROG  No. 

TIMES  THE  FROG 

SHORT 

LEAD. 

THEORETICAL 
LKAD. 

Feet. 

Inches. 

Feet.    Inches. 

4 

9^ 

38 

0 

38         o 

5                     9l/2 

47 

6 

47         6 

6                     9/2 

57 

0 

57         o 

7 

9/2 

66 

6 

66         6 

8 

9 

72 

0 

76         o 

9 

8'/2 

76 

6 

85         6 

10 

S/2 

85 

0 

95         o 

n 

8 

88 

0 

104         6 

12                              8 

96 

o 

114         o 

15                     8 

1  20 

0 

142         6 

In  this  table,  in  the  second  column,  are  the 
number  of  times  the  frog  number  is  to  be 
multiplied  to  obtain  the  short  lead,  and  in  the 
third  column  are  the  short  leads  so  obtained, 
the  last  column  showing  the  theoretical  leads 
for  comparison. 

It  will  be  observed  that  the  lead  is  not  short- 
ened for  frogs  less  than  No.  8,  it  not  being 
necessary  to  do  so,  as  the  theoretical  curve  at 
the  heel  of  the  switch  is  more  than  5  or  5^ 
inches  from  the  gauge  of  the  main  rail  for  frogs, 
*  less- than  No.  8. 


THE  SHORTENED,    OR  PRACTICAL,   LEAD,          IJ 

In  this  consideration  the  shortened  lead  is  ob- 
tained by  moving  the  heel  of  the  switch  in  the 
direction  of  the  frog  to  the  point  on  the  turnout 
curve  where  the  distance  from  the  main  rail  to 
the  theoretical  curve  is  about  equal  to  5  or  5 J 
inches,  the  distance  between  the  frog  and  the 
heel  of  the  switch  point  corresponding  to  the 
stub  lead  for  a  throw  of  5  or  5^-  inches,  the 
switch  point,  15  or  18  feet  long,  being  added  to 
complete  the  short  lead. 

Although  the  shortened  leads  as  here  given 
Are  very  good,  it  may  be  well  to  vary  from  them 
whenever  it  can  be  done  without  detriment  to 
the  efficiency  of  the  turnout,  in  order  to  avoid  a 
waste  of  rail  by  cutting,  as  what  is  given  here  as 
short  leads  is  merely  to  show  to  what  extent  the 
theoretical  lead  can  be  safely  reduced,  for  these 
short  leads  are  not  arbitrary  ones  which  should 
not  be  varied  from  when  it  is  better  to  do  so, 
Any  variation,  however,  will  depend  upon  the 
length  of  the  switch  point  or  split  switch,  the 
distance  from  point  to  toe  of  frogs,  and  also  upon 
what  lengths  of  rail  are  available  for  the  turnout. 

The  variety  of  distances  from  point  to  toe  of 
frogs  and  different  lengths  of  switch  points  make 
it  difficult  to  even  suggest  any  definite  lengths 
of  rail  between  the  frog  and  switch  to  meet  the 
requirements  of  various  locations  and  conditions. 


18 


PRACTICAL  SWITCH  WORK. 


However,  in  the  following  table  is  an  illustra- 
tion of  how  the  economical  use  of  material  can 
be  observed  without  varying  much  from  the 
shortened  lead  as  given  in  Table  No.  3,  the 
switch  point  in  this  case  being  18  feet  long  ajid 
frog  from  point  to  toe  7^-  feet : 

TABLE  No.  4. 
ADAPTING  LEAD  TO  THE  MATERIAL. 


MATERIAL. 

FROG 

SHORT 

No. 

LKAD. 

Switch. 

Rails. 

Frog. 

Total  Lead. 

Ft.     In. 

Feet. 

Feet. 

Ft.     In. 

Ft.    In. 

6 

57    o 

18 

30 

7      6 

55     6 

7 

66     6 

18 

25      +15 

7      6 

65    6 

8 

72     o 

18 

30      +  '5 

7      6 

70    6 

9 

78    o 

18 

27^  +  25 

7      6 

78    o 

10 

85    o 

18 

30     +30 

7      6 

85    6 

ii 

90    o 

18 

50     +I3/^ 

7      6 

89    o 

12 

96    o 

18 

60     4-15 

7      6 

100    6 

15 

120      0 

18 

9° 

7      5 

115    6 

For  a  short  lead  for  a  No.  8  frog,  which 
would  be  about  72  feet  long,  use  a  rail  30  feet 
long  and  cut  one  into  two  pieces  15  feet  long. 
Those  pieces,  making  45  feet,  are  all  that  are  nec- 
essary between  the  switch  and  the  frog,  and 
with  the  1 8-foot  switch  point  and  7^-  feet  from 
point  to  toe  of  frog,  make  70  feet  6  inches, 
which  is  a  good  lead  and  can  be  used  without 


THE  SHORTENED,   OR  PRACTICAL,  LEAD.          ig 

any  hesitation.  For  No.  11  frog,  two  25-foot 
rails  and  a  1 5-foot  piece,  making  a  lead  of 
90^  feet,  is  a  preferable  variation  from  88  or 
90  feet.  The  object  should  be  to  make  but 
one  cut  to  get  .two  pieces  to  fill  out. 

So  long  as  the  lead  of  a  No.  8  is  not  less  than 
69  or  70  feet  it  is  very  good,  but  it  should  not  be 
less  than  69  feet  if  it  can  be  avoided. 

If  the  switch  point  is  15  instead  of  1 8  feet, 
then  use  two  25-foot  rails,  which  would  make 
the  lead  72  feet  6  inches.  Each  case  should  de- 
termine to  what  extent  the  material  can  be 
adapted,  it  being  permissible  to  vary  a  few  feet 
either  way  from  the  shortened  leads  as  given, 
but  for  a  No.  8  frog  it  should  not  be  more  than 
73  feet. 

Instead  of  cutting  the  3O-foot  rail  exactly 
into  two  pieces  1 5  feet  long,  to  be  placed  be- 
tween the  frog  and  switch,  cut  one  14  feet  1 1 
inches  and  the  other  1 5  feet  I  inch  long,  and 
place  the  longer  piece  in  the  curved  and  the 
shorter  in  the  straight  track.  This  will  enable 
the  heel  of  the  switch  points  to  be  exactly  op- 
posite each  other,  and  the  joint  ties  will  be  square 
across  the  tracks. 

All  cases  cannot,  of  course,  be  adapted  to  the 
material,  owing  to  the  difficulty  to  obtain  rails  of 
suitable  length,  but  in  shortening  the  lead  the 


2O  PRACTICAL  SWITCH  WORK. 

object  should  be  to  avoid  a  waste  of  material, 
and  at  the  same  time  to  adhere  as  closely  as  pos- 
sible to  the  short  leads  given  in  Table  No.  3. 

For  any  short  lead  use  the  formula — 

l=2n(g—  -i/Ji) 
and  add  the  length  of  the  switch  point. 

If  the  switch  is  less  than  15  feet,  say  10  or  12 
feet,  assume  a  throw  less  than  5  inches,  but  in 
no  case  less  than  4  inches. 

Note  that  in  Table  No.  4,  adapting  the  lead 
to  the  material,  the  lead  of  Nos.  9  and  n  frogs 
has  been  increased. 


TURNOUTS  FROiM  CURVES. 

The  preceding  pages  have  referred  only  to 
turnouts  from  a  straight  track. 

It  happens  frequently  that  it  is  necessary  to 
put  in  a  turnout  from  a  curve,  and  the  first  and 
very  natural  question  is,  whether  the  lead  suit- 
able for  a  turnout  from  a  straight  track  will  do 
also  for  one  from  a  curve,  no  difference  how 
sharp  it  is,  or  upon  which  side  of  the  curve  the 
turnout  may  be.  The  answer  to  this  is  that  the 
same  lead  can  be  used  whether  the  turnout  is 
from  a  straight  track  or  from  a  curve,  as  the 
lead,  theoretically,  when  the  turnout  is  from  a 
curve,  is  only  a  few  inches  different  in  length 
from  what  it  is  when  it  is  from  a  straight  track. 

Making  the  lead  longer  when  the  turnout  is 
from  the  inside  of  a  curve  is  generally  resorted 
to  for  the  purpose  of  reducing  the  curvature  of 
the  turnout,  and,  without  reflection,  it  would 
seem  to  be  the  proper  way  to  overcome  the 
difficulty,  but  it  does  not  do  so  unless  a  frog  of 
higher  number,  which  requires  a  longer  lead,  is 
used.  A  frog  of  higher  number  corresponding 
to  the  desired  lead  should  be  used,  as  the  longer 
lead  is  for  a  frog  of  smaller  angle,  the  remedy 
(21) 


22  PRACTICAL  SWITCH 

being  in  the  frog  of  less  angle  and  longer  lead, 
and  not  in  the  increased  lead  without  a  differ- 
ent frog. 

TURNOUTS  FROM  THE  INSIDE  OF  CURVES. 

When  a  turnout  is  from  a  curve,  its  curvature 
is  greater  or  less  than  it  would  be  from  a  straight 
track,  according  to  whether  it  is  from  the  inside 
or  outside  of  the  curve.  If  it  is  from  the  inside, 
it  will  be  greater ;  if  from  the  outside,  it  will  be 
less  than  it  would  be  from  a  straight  track. 


No.  2 


For  example :  a  No.  8  frog  in  a  straight  track 
'has  for  the  turnout  about  a  gj-degree  curve. 
The  same  frog  from  the  inside  of  a  curve  has  for 
the  turnout  a  curve  equal  to  the  degree  of  the 
main  track  curve  added  to  9^,  the  degree  of  the 
curve  for  a  No.  8  frog. 

Suppose  the  main  track  curve  is  4  degrees ;  by 
adding  9^  degrees  we  have  i^  degrees  as  the 
curvature  of  the  turnout  curve. 

The  turnout  being  from  the  inside  of  the  4- 
degree  curve  increases  the  curvature  of  the  turn- 
out from  9^  to  1 3^  degrees. 


TURNOUTS  FROM  CURVES.  2 3 

If  the  main-track  curve  should  be  6  degrees, 
the  turnout  curve  would  be  15^  degrees,  or  9^ 
added  to  6  degrees. 

Before  making  a  connection  from  the  inside 
of  a  curve,  first  ascertain  what  the  degree  of  the 
main-track  curve  is.  The  method  for  doing  this 
is  given  under  the  heading,  "To  Ascertain  the 
Degree  of  Curvature." 

Having  ascertained  the  degree,  then  decide 
upon  the  number  of  the  frog  to  be  used  or  how 
sharp  a  turnout  curve  is  desired. 

To  ascertain  what  is  the  degree  of  curvature 
through  a  frog  upon  a  curve  refer  to  Tables  Nos. 
5  and  6.  Add  the  degree  of  the  curve  through 
the  frog  in  a  straight  track  to  the  degree  of  the 
curve  of  the  track  in  which  the  frog  is  to  be 
placed,  and  their  sum  will  be  equal  to  the  degree 
of  the  turnout  curve.  If  the  sum  of  these  two 
gives  a  curvature  too  great,  then  use  a  frog  of  a 
higher  number  to  give  the  curvature  desired. 

Great  care  should  be  taken  not  to  have  a  frog 
upon  the  inside  of  a  curve  that  will  make  the 
turnout  curve  so  sharp  that  it  will  always  be  a 
source  of  annoyance  and  expense  from  the  track 
spreading  or  derailments. 

There  is  a  limit  to  the  degree  of  curvature  in 
turnouts.  Ordinarily  no  frog  should  be  placed 
upon  the  inside  of  a  curve  which  will  make  the 


24  PRACTICAL  SWITCH  WORK. 

turnout  curve  greater  than  about  16  degrees,  01 
that  suitable  to  a  No.  6  frog,  unless  engines 
especially  adapted  to  very  sharp  curvature  are 
used.  But  for  engines  weighing  50  tons  or 
more  it  would  be  better  to  have  no  turnout 
curve  sharper  than  10  or  12  degrees,  if  it  were 
possible. 

TURNOUTS  FROM  THE  OUTSIDE  OF  CURVES. 

By  reference  to  diagrams  Nos.  2  and  3,  it  is 
evident  that  the  curvature  of  a  turnout  from  the 


outside  of  a  curve  is  less  than  that  from  the  in- 
side of  a  curve  or  from  a  straight  track. 

To  find  the  degree  of  the  turnout  curve  wher* 
it  is  from  the  outside,  take  the  difference  be- 
tween the  degree  of  the  main-track  curve  and 
the  degree  of  the  curve  of  the  frog,  as  given  in 
Table  No.  6. 

Suppose  the  curvature  of  the  main  track  is  4 
degrees  and  the  frog  is  a  No.  8,  the  curva- 
ture suitable  to  which  is  9^  degrees,  the  differ- 
ence between  9^  degrees  and  4  degrees  is  5} 
degrees,  which,  in  this  case,  is  the  degree  of  a 


TURNOUTS  FROM  CURVES,  2Jf 

turnout  curve  turning  to  the  outside  of  the  4- 
degree  curve. 

If  the  curvature  of  the  main  track  is  about  10 
degrees,  the  curvature  of  the  turnout  would  be 
very  light,  practically  a  straight  line,  the  differ- 
ence being  only  about  a  half  degree. 

A  No.  6  frog  from  the  outside  of  an  8-degree 
curve  will. have  about  the  same  degree  of  curva- 
ture as  a  No.  8  frog  from  a  straight  track;  that 
is,  17  degrees  less  8  degrees,  equal  to  9  de- 
grees. 

This  is  worth  remembering  when  putting  in  a 
turnout  at  the  heel  of  a  No.  8  frog  to  turn  to 
the  outside.  If  a  No.  8  frog  is  used  in  such  a 
case,  the  curvature  through  it  will  be  less  than 
that  of  the  frog  ahead ;  whereas,  if  a  No.  6  is 
used  its  curve  will  be  about  the  same  as  that  of 
the  No.  8,  and  it  will  make  a  much  better  turn- 
out. 

If,  however,  it  is  intended  to  connect  with  a 
parallel  track,  then  use  a  No.  8,  or  the  same 
number  as  the  other  frog,  and  put  it  in  line  with 
the  other  frog,  just  as  in  the  case  of  a  ladder 
track. 

The  following  tables  give  the  degree  of  the 
turnout  curve  when  the  frog  is  upon  either  the 
inside  or  the  outside  of  curves  from  I  to  9  de- 
grees. 


l6  PRACTICAL  SWITCH 

TABLE  No.  5. 
WHEN  FROG  is  UPON  THE  INSIDE  OF  THE  CURVE. 


FROG 

No. 

CURVE  FROM 
STRAIGHT 
LINE. 

i° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Degrees. 

Deg. 

Deg- 

Deg. 

Deg. 

Deg. 

Deg. 

Deg. 

D"g. 

Deg. 

6 

17 

18 

19i 

20 

21 

22 

?3 

24 

25 

26 

7 

13^ 

I5% 

l6% 

19/4 

20^ 

21% 

8 

9/4 

10  % 

11% 

12% 

13% 

14% 

I5/^ 

16% 

I7/^ 

I$% 

9 

1% 

8% 

9% 

J0% 

11% 

12% 

*3% 

14% 

I$% 

}6% 

10 

6 

7 

10 

II 

12 

13 

H 

15 

ii 

5 

6 

7 

9 

IO 

II 

12 

13 

14 

12 

4^ 

5t 

6 

7x 

8 

9t 

10 

II 

12 

I3i 

15 

21/2 

31/2 

4% 

51/2 

6% 

7/2 

8% 

9% 

xoK 

ii# 

TABLE  No.  6. 
WHEN  FROG  is  UPON  THE  OUTSIDE  OF  THE  CURVE. 


FROG 
No. 

CURVE  FROM 
STRAIGHT 
LINE. 

i° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Degrees. 

Deg. 

Deg. 

De?. 

Deg. 

Deg. 

Deg. 

Deg. 

Deg. 

D"g. 

4 

5 

38^ 
24^ 

37/2 
23  # 

36M 
22X2 

35M 

21^ 

34/2 
20^ 

33/2 
I9# 

32  K 
18^ 

31/2 
17^ 

30^ 
16^ 

29% 
15^ 

6 

17 

16 

15 

14 

13 

12 

ii 

10 

9 

8 

7 

1254 

nJ/2 

IO1/, 

8« 

7^ 

6^ 

5/2 

& 

3J4 

8 

9^ 

8^2 

7x/2 

6l/2 

5/2 

4/2 

3/2 

2/2 

1/2 

9 

7/2 

6y2 

5/2 

4/2 

3/2 

2/2 

1/2 

10 

6 

5 

4 

3 

2 

I 

In  the  first  column  are  the  frog  numbers;  in 
the  next  is  the  degree  of  curvature  for  each  frog 
when  the  turnout  is  from  a  straight  line ;  in  the 
other  columns  is  given  for  each  frog  the  degree 
of  curvature  when  the  turnout  is  from  any  curve 
from  i  to  9  degrees. 

To   use   these   tables,  suppose   it   should  be 


TURNOUTS  FROM  CURVES.  2 J 

necessary  tcrput  in.a  turnout  from  the  inside  of 
a  6-degree  curve  and,  at  the  same  time,  it  should 
be  desirable  that  the  curvature  of  the  turnout 
should  not  exceed  12  degrees,  what  frog  should 
be  used  ?  Look  in  Table  No.  5,  and  in  the  eighth 
column,  under  6  degrees,  12  is  found ;  opposite 
12,  in  the  first  column,  is  10;  10,  then,  is  the 
number  of  the  frog  to  be  used.  For  any  desired 
curvature  for  any  other  frog  proceed  in  the 
same  manner. 

Suppose  again,  that  it  is  desired  to  know  the 
curvature  of  a  No.  8  frog  upon  the' inside  of  a 
7-degree  curve.  Look  in  the  first  column,  Table 
No.  5,  for  No.  8  frog,  and  opposite  it,  in  the  ninth 
column,  under  7  degrees,  find  i6J  degrees,  which 
is  the  degree  of  the  desired  curve.  Any  other 
degree  is  found  in  the  same  manner. 

Again,  this  question  may  arise :  Is  it  advis- 
able to  have  a  No.  6  turnout  upon  the  inside  of 
a  3-degree  curve  ?  The  answer  is,  No ;  because 
by  reference  to  Table  No.  5  the  curvature  will 
be  found  to  be  about  20  degrees,  which  is  too 
sharp  for  ordinary  service. 

Referring  to  Table  No.  6,  suppose  a  turnout  is 
to  be  upon  the  outside  of  a  6-degree  curve,  what 
frog  will  give  a  turnout  curve  not  to  exceed  the 
curvature  of  main  track  ?  A  No.  7  frog  will  do 
it.  Look  in  the  eighth  column,  Table  No.  6, 


28  PRACTICAL  SWITCH 

and  -under  6  degrees,  6^  degrees  is  found  oppo- 
site No.  7  in  the  first  column.  No.  7,  therefore, 
is  the  frog  which  should  be  used,  6J  degrees  be- 
ing the  nearest  degree  of  curvature. 

Suppose  again,  that  it  is  desired  to  know  the 
curvature  of  a  No.  8  frog  upon  the  outside  of  a 
4-degree  curve.  Find  No.  8  frog  in  first  column, 
Table  No.  6,  and  opposite  it,  under  4  degrees, 
in  sixth  column,  is  5^  degrees;  5^  degrees  is, 
therefore,  the  curvature  desired. 

When  a  turnout  is  upon  the  outside  of  a 
curve  it  is  preferable  to  use  a  frog  which  will 
give  a  turnout  curve  somewhat  similar  in  degree 
to  that  of  the  main  curve,  instead  of  using  oive 
which  will  make  the  turnout  curve  flat  as  com- 
pared to  the  main  curve.  Frogs  of  high  num- 
bers, that  is,  those  above  a  No.  8  or  10,  should, 
therefore,  not  be  used  ordinarily  in  such  cases. 

In  ordinary  practice  there  are  not  many  cases, 
whether  upon  the  inside  or  outside  of  a  curve, 
which  cannot  be  fully  met  by  using  a  No.  6,  8, 
or  10  frog,  so  that  it  is  rarely  necessary  to  use 
higher  than  these  numbers,  unless  high  speed  is 
attained  or  the  main-track  curve  is  very  sharp. 


THE   STUB    LEAD. 

The  stub  lead,  like  the  point  lead,  is  measured 
along  the  straight  rail — A  to  B. 

There  is  no  simple  rule  for  obtaining  the  stub 
lead  for  all  frogs  and  gauges,  as  is  the  case  with 
the  point  lead.  This  is  on  account  of  there 
being  so  many  different  throws  for  the  switch 
rails. 

The  "throw"  of  a  stub  switch  is  the  distance 
the  slide  or  moving  rail  moves  at  the  head-block 


No.  4. 


A,  ana  every  throw  requires  a  different  lead, 
The  throws  for  standard  gauges  are  ^,  $%,  or  $$ 
inches — $  inches  predominating. 

The  lead  for  a  stub  switch  for  4  feet  8£  inch 
and  4  feet  9  inch  gauges  is,  approximately,  6f 
times  the  frog  number  for  5-inch  throw,  and  6£ 
times  the  frog  ntlmber  for  5f-inch  throw. 

In  the  following  table  are  leads  which,  al- 
though   approximate,    are   nearly    correct.      In 
Table  No.  9  are  given  the  correct  leads. 
(29) 


PRACTICAL  SWITCH  WORK. 


TABLE  No.  7. 

APPROXIMATE  STUB  LEADS,  4  FEET  8%  INCH  AND 
4  FEET  9  INCH  GAUGES. 


S-INCH  THROW. 

5%-lNCH  THROW. 

Frog 
No. 

Times. 

Lead. 

Frog 
No. 

Times. 

Lead. 

Feet.    Inches. 

i    Feet.    Inches. 

6 

6^ 

40        6 

6 

6^   !      39         0 

7 

63^ 

47        3 

7 

6^ 

45         ^ 

8 

63^ 

54        o 

8 

6* 

52         o 

9 

63^ 

60        9                9 

6^ 

58         6 

10 

63^ 

67        6 

10 

6^ 

65        o 

II 

6# 

74        3 

ii 

6J4 

71        6 

•  12 

6^ 

81        o 

12 

6/2 

78        o 

The  stub  lead  should  not  be  shortened;  it 
and  the  theoretical  length  of  switch  rail  should 
be  equal,  or  nearly  so,  to  the  full  theoretical 
lead. 

A  formula  by  which  the  stub  lead  can  be  cal . 
culated  for  any  gauge,  throw,  and  frog,  is : — 
Stub  lead,  or  /  —  211  (g    -  |/Jf/),  in  which 
/  equals  stub  lead, 
n  equals  frog  number, 
g  equals  gauge, 
/  equals  throw. 

This  means  that  the  stub  lend  is  equal  to  the 
gauge,  minus  the  square  root  of  the  product  of 
the  gauge  and  throw,  multiplied  by  twice  the 
number  of  the  frog. 


THE  STUB  LEAD.  31 

To  make  this  formula  easily  used,  in  the  fol- 
lowing table  it  is  partially  worked  out  for  the 
gauges  and  throws  most  generally  used,  it  only 
remaining  to  multiply  the  distances  in  the  table 
following  by  twice  the  frog  number  to  obtain 
the  stub  lead  for  any  frog. 

TABLE   No.  8. 


3  FEET  GAUGE. 


INCH  GAUGE.  14  FT.  9  IN.  GAUGE. 


Throw. 

(g-l/gt) 

Throw. 

(g-Vit) 

(g-/gt) 

Inches. 

Feet.    Inches. 

Inches. 

Feet.     Inches. 

Feet.     Inches. 

3 

2            83^ 

5 

3          3#' 

3           4 

3/2 

2            8# 

5/2 

3          3 

3         3X 

4 

2        8X 

5U 

3           2>£ 

3         3 

For  any  stub  lead  multiply  the  distance  oppo- 
site the  throw  by  twice  the  frog  number. 

What  is  the  stub  lead  of  No.  9  frog,  4  feet 
8£  inch  gauge  and  5-inch  throw?  Multiply  3 
feet  3f  inches,  opposite  5-inch  throw,  by  twice 
the  frog  number,  or  1 8,  and  we  have  59  feet  7 
inches  as  the  stub  lead. 

Give  stub  lead  of  No.  8  frog,  4  feet  9  inch 
gauge  and  5f-inch  throw.  3  feet  3  inches,  op- 
posite 5f-inch  throw,  multiplied  by  16,  or  twice 
No.  8  frog,  is  equal  to  52  feet,  or  the  stub  lead 
desired. 


PRACTICAL  SWITCH  WORK. 


The  stub  lead  need  not  be  exact.  The  same 
liberty  in  departing  from  it,  however,  cannot  be 
taken  as  with  the  theoretical  point  lead,  and,  so 
far  as  it  can  be  done,  the  calculated  stub  lead 
should  be  adhered  to ;  not,  however,  to  the  ex- 
tent of  wasting  rail  by  cutting  so  as  to  get  the 
exact  lead. 

Do  not  use  a  stub  lead  for  frogs  higher  than 
10  or  12,  as  the  curvature  of  the  switch  rail  will 
be  greater  than  the  curvature  from  the  head- 
block  to  the  frog  point. 

The  leads  given  in  Table  No.  7  are  only  ap- 
proximately correct.  If  the  correct  lead  is  de- 
sired it  can  be  found  in  the  table  bejow. 

TABLE  No.  9. 
CORRECT  STUB  LEADS  FOR  DIFFERENT  THROWS. 


FROG 

4  FEET  S%  INCHES. 

4  FEET  9  INCHES. 

SWITCH 

No. 

I 

RAIL. 

5  In. 

5#>. 

5%  In. 

5  In. 

5^  In. 

5K  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Feet. 

4 

26  6 

25  II 

25  « 

26  9 

26  2 

26  o 

12 

5 

33  i 

32  5 

32   I 

33  5 

32  9 

32  6 

15 

6 

39  9 

38  ii 

38  6 

40   2 

39  4 

39  o 

18 

7 

46  4 

45  5 

44  ii 

46  10 

45  10 

45  6 

21 

8 

52  TI 

51  10 

51  4 

53  6 

52  5 

52  o 

24 

9 

59  7 

58  4 

57  9 

60   2 

59  o 

58  6 

26 

10 

66  2 

64  10 

64   2 

66  ii 

65  6 

65  o 

26 

II 

72  9 

71  4 

70  7 

73  7 

72  o 

7i  6 

26 

12 

79  5 

77  9 

77  o 

80  3 

78  7 

78  o 

26 

SWITCH   OR  MOVING  RAILS. 

One  of  the  things  in  regard  to  which  track- 
men are  generally  ignorant  is  the  correct  length 
of  the  switch  or  moving  rail  of  a  stub  switch. 

It  is  not  unusual  to  see  it  the  same  length  for 
all  frogs  without  regard  to  what  the  throw  may 
be. 

Practically  it  does  not  make  much  difference, 
except  in  frogs  less  than  No.  8,  but  every  fore- 
man ought  to  know  what  is  the  proper  length 
and  how  to  obtain  it. 

A  good  moving  rail  is  made  by  cutting  a  few 
inches  off  a  3O-foot  rail. 

It  should  always  be  spiked  to  not  less  than 
3  cross-ties  and  not  less  than  4  feet  from  the 
end  of  the  rail,  no  difference  for  what  frog  or 
throw  it  may  be,  nor  what  may  be  given  as 
the  correct  theoretical  length  of  the  moving 
rail. 

The  spiking  point  nearest  the  head-block  is, 
in  theory,  the  beginning  of  the  turnout  curve, 
and  to  that  point — that  is,  to  the  point  of  the 
turnout  curve — so  far  as  practicable,  the  rails 
should  be  spiked  solid,  but  beyond  it,  held  to 

3  (33) 


54  PRACTICAL  SWITCH  WORK. 

gauge  only  by  the  switch-rods,  they  should  br> 
left  to  adjust  themselves  to  conform  to  the  turn- 
out curve. 

For  every  different  frog  and  throw  the  di<i- 
tance  from  the  head-block  to  the  last  spiking 
point  is  different,  and  this  variable  distance  is 
called  the  theoretical  length  of  the  moving  rail 
The  theoretical  moving  rail  for  a  No.  10  frog 
and  5f-inch  throw  is  30  feet,  but  as  rails  are 
only  30  feet  long  this  theoretical  length  must  be 
reduced  to  about  26  feet,  which  is  about  the 
longest  practicable  length  of  moving  rail. 

The  following  is  a  table  of  practicable  length 
of  the  moving  rail 

TABLE  No.  10. 

FOR  4  FEET  8^  INCHES,  4  FEET  9  INCHES,  3  FEET 
GAUGES. 


4  FEET 

8*4  AND  4  FEET  9  INCHES. 

3  FEET. 

FROG  No. 

5  1 

nches. 

5^  Inches. 

4  Inches. 

Feet. 

Inches. 

Feet. 

Feet. 

4 

It 

0 

12 

8 

5 

13 

9 

15                   10 

6 

16 

6 

18                           12 

7 

19 

3 

21 

H 

8 

22 

o 

24 

16 

9 

24 

9 

26 

18 

10 

26 

o 

26 

20 

ii 

26 

0 

26 

22 

SWITCH  OR  MOVING  RAILS.  35 

This  may  be  condensed  into  the  following 
rule :  For  4  feet  8^  and  4  feet  9  inch  gauges  and 
5-inch  throw,  the  length  of  the  moving  rail  is 
2f  (or  2.75)  times  the  frog  number,  and  for  5f- 
inch  throw  it  is  3  times  the  frog  number. 

For  3  feet  gauge  and  4-inch  throw  it  is  twice 
the  frog  number. 

A  few  inches  less  than  30  feet  is  a  good  length 
of  rail  to  make  a  moving  rail,  for  the  reason  that 
there  are  always  on  hand  old  3<>foot  rails  with 
battered  ends  which  can  be  cut  off. 

There  is  no  advantage  in  using  in  a  stub 
switch  a  frog  higher  than  No.  10  or  1 1,  because, 
it  being  impossible  to  make  the  moving  rails  the 
required  theoretical  length  for  frogs  above  these 
numbers,  the  curvature  of  tjie  moving  rails  would 
be  sharper  than  the  turnout  curve  from  the  head- 
block  to  the  point  of  the  frog,  and  what  would 
be  gained  by  a  frog  of  high  number  or  small 
angle  with  decreased  curvature  would  be  lost  by 
the  increased  curvature  of  the  moving  rails. 


THE  FROG  NUMBER. 

The  "  number "  of  a  frog  means  the  same 
as  what  is  called  the  "  proportion  "  of  a  frog. 
A  I  to  7  frog  is  in  the  "  proportion,"  properly 
the  ratio,  of  I  foot  wide  to  7  feet  long,  and  is  the 
same  as  a  No.  7 ;  or  a  i  to  10  the  same  as  a  No. 

10. 

The  number  of  a  frog  corresponds  to  its  length 
from  point  to  heel  divided  by  its  width  at  the 
heel  measured  from  gauge  to  gauge  of  the  rails 
forming  the  frog  angle. 

It  is  important  that  the  trackman  should  be 
able  to  distinguish  one  number  of  frog  from  an- 
other, and  he  should  bear  in  mind  that  all  frogs  of 
the  same  width  at  the  heel  may  not  be  the  same 
number.  The  width  at  the  heel  is  greater  or 
less  according  to  the  distance  from  the  point  to 
the  heel ;  and  the  way  to  do  in  every  case  of  un- 
certainty is  to  measure  the  frog  as  explained 
on  pages  37,  38,  and  39. 

There  is  no  uniform  length  of  frog  from  point 
to  heel;  that  distance  is  therefore  liable  to  be  as 
various  as  there  are  frog  makers. 

A  I  to  8  frog,  or  a  No.  8,  at  8  inches  from  the 
theoretical  frog  point  in  the  direction  of  the  heel 
(36) 


THE  FROG  NUMBER.  37 

is  I  inch  wide,  and  at  8  feet  it  is  i  foot  wide,  or 
I  wide  to  8  long,  whether  it  is  inches  or  feet, 
and  it  is  always  measured  from  gauge  to  gauge. 

A  i  to  10,  or  No.  10,  at  10  inches  from  the 
point  is  i  inch  wide,  and  at  10  feet  it  is  one  foot 
wide,  or  i  wide  to  10  long. 

One  way  to  obtain  the  number  of  any  frog  is 
to  first  ascertain  accurately  where  the  theoretical 
point  of  the  frog  is,  it  being  the  intersection  of 
the  sides  of  the  frog  as  shown  and  explained  on 
page  43 ;  then  take  a  foot  rule  and  find  where 
the  frog  measures  exactly  4  inches  wide,  from 
gauge  to  gauge,  C  to  D,  back  of  the  point,  as 
shown  in  the  diagram  : — 


From  where  it  is  4  inches  wide  measure  the 
distance  to  the  intersection  of  the  gauge  lines  at 
the  theoretical  frog  point  A,  and  divide  this  dis- 
tance in  inches  by  4  inches,  the  width,  and  as 
many  times  as  it  is  greater  than  the  4  inches  in 
width  will  be  equal  to  the  frog  number. 

Twenty-four  inches  divided  by  4  inches  is  equal 
to  6,  or  a  No.  6  frog. 


38          '  PRACTICAL  SWITCH  WORK. 

Thirty-two  inches  divided  by  4  inches  is  equal 
to  3,  or  a  No.  8  frog. 

The  following  is  a  table  of  the  distance  for 
different  frogs  from  where  the  width  is  4  inches 

to  the  theoretical  point  A. 

\ 
TABLE   No.    ii. 

MEASUREMENTS  TO  OBTAIN  FROG  NUMBER. 


Frog  No. 

Distance. 

Width. 

Frog  No.! 

Distance. 

Width. 

Inches,     i      Inclu  s. 

Inches. 

Inches. 

4 

l6                  4 

9 

36 

4 

5 

20 

4 

10 

40 

4 

6 

24               4 

ii 

44 

4 

7 

28               4         [I      12       | 

48 

4 

8 

32 

4                15 

60 

4 

The  frog  number  can  also  be  obtained  in  an- 
other way.  Take  a  lead-pencil,  or  a  stick  about 
as  long  or  a  little  longer  than  a  pencil,  and  find 
where  the  width  of  the  frog,  gauge  to  gauge,  is 
exactly  equal  to  the  length  of  the  stick  or  pen- 
cil ;  from  this  point,  by  trial,  find  how  many 
times  greater  than  the  stick  or  pencil  the  dis- 
tance is  to  the  theoretical  point  A. 

If  it  is  6  times  greater,  the  frog  is  a  No.  6 ;  if 
8  times,  it  is  a  No.  8,  and  so  on. 

By  a  careful  use  of  the  pencil  or  stick  the 
frog  number  can  readily  be  ascertained. 


THE  FkOG  NUMBER.  39 

Another  way  is  to  take  the  frog-boards  re- 
ferred to  on  page  45,  and  place  them  one  by  one 
upon  the  frog  until  that  one  is  found  whose 
sides  coincide  with  the  gauge  lines  of  the  frog, 
and  the  board  corresponding  to  the  frog  being 
numbered,  the  frog  number  is  at  once  known. 

Another  way  is  to  divide  the  total  length  of 
the  frog  from  heel  to  toe  by  the  sum  of  the 
vridth  at  the  heel  and  at  the  toe.  For  example, 
if  the  total  length  is  15  feet,  or  180  inches,  and 
the  width  at  the  heel  8  inches  and  at  the  toe 
y  inches,  their  sum  would  be  15  inches;  divid- 
ing 1 80  by  15  the  frog  would  be  No.  12,  as  12 
limes  15  are  equal  to  180. 

In  measuring  at  the  toe  the  distance  between 
the  inside  of  the  rails  should  be  taken,  whereas 
at  the  heel  the  distance  to  be  used  is  between 
the  outside  of  the  rails,  or  the  gauge  lines  in 
both  cases. 


THE  FROG  ANGLE. 

It  would  not  be  necessary  for  the  trackman 
to  know  anything  about  the  frog  angle,  except 
to  prevent  his  confusing  it  with  the  "propor- 
tion" of  a  frog  and  also  the  frog  number. 

What  is  called  the  "  proportion"  of  a  frog  i:. 
the  measure  of  the  spread  or  divergence  of  the1 
two  sides  of  the  frog  in  inches  or  feet ;  as,  for 


example,  in  a  No.  8  frog,  at  every  8  inches 
from  the  point  in  the  direction  of  the  heel,  the 
distance  across  is  i  inch,  or  at  every  8  feet  it  is 
I  foot,  or  in  the  " proportion"  of  i  to  8.  Cor- 
rectly speaking,  it  is  the  ratio  of  i  tc  8. 

The  frog  angle  is  also  the  spread  or  divergence 

of  the  two  sides  of  the  frog,  but  the  expression 

for  its  measure  is  in  terms  of  the  degree  and 

minute,  which  expressions  are  used  only  in  con- 

(40) 


THE  FROG  ANGLE.  .\\ 

nection  with  the  surveying  instrument  and  cal- 
culations, and,  therefore,  of  no  important  use  to 
the  foreman  in  his  practical  work. 

In  explanation  of  the  word  degree,  as  it  re- 
lates to  a  frog  (see  diagram  No.  6),  every  circle, 
however  large  or  small,  is  divided  into  360  equal 
parts  or  spaces,  each  of  which  is  called  a  "de- 
gree." 

Beginning  at  D  in  the  diagram,  from  D  to  E 
it  is  90  degrees,  from  D  to  F  180  degrees,  from 
D  to  G  270  degrees,  and  from  D  to  D  360  de- 
grees, completing  the  circle.  So  if  the  lines  A 
B  C  represent  the  angle  of  a  frog,  the  point  of 
which  is  in  the  centre  of  the  circle,  the  amount 
of  the  divergence  or  angle  of  its  two  sides  will 
be  as  many  degrees  as  are  included  between  the 
the  sides  A  B  and  A  C,  the  number  of  the 
degrees  being  different  for  each  frog  number. 

Below  is  a  table  of  frog-angles  corresponding 
to  frogs  of  different  number. 

TABLE  No.  12. 
FROG  ANGLES. 


Frog  No. 

Frog  Angle. 

Frog  No. 

Frog  Angle. 

4 

14°    15 

j 
9 

6°    22' 

5 

II      25 

10                    5     44 

6        I            9     32 

II 

5     12 

7                    8     10 

12 

4    46 

8                   7    09 

15 

4     24 

42  PRACTICAL  SWITCH  WORK. 

In  explanation  of  the  table,  14°  15'  means 
14  degrees  and  15  minutes,  and  11°  25' means 
ii  degrees  and  25  minutes. 

If  the  diagram  represented  a  No.  6  frog,  for 
example,  its  spread  or  divergence  would  be 
about  9^  of  the  90  degrees  from  D  to  E. 

The  numbers  in  the  column  under  "  Frog 
Angle"  represent  the  degrees  and  minutes,  the 
latter  being  the  expression  of  the  measure  of 
anything  less  than  a  degree.  The  angle  of  No.  4 
frog,  for  example,  is  14  degrees  and  15  minutes, 
or  14^  degrees,  15  being  one-fourth  of  60,  the 
number  of  minutes  in  a  degree. 

Any  difference  in  the  gauge  of  the  track  does 
not  affect  the  frog  angle,  the  angle  of  a  No.  8 
frog  in  a  4  feet  9  inch  gauge  being  the  same 
as  for  the  same  frog  in  a  3  feet  gauge. 


THE  FROG  POINT. 

There  is  perhaps  nothing  in  the  detail  of 
switch  work  which  the  trackman  is  so  apt  to 
regard  as  unimportant,  or  of  which  he  knows  so 
little  and  yet  which  is  so  important,  as  to  properly 
understand  what  is  the  theoretical  point  of  the 
frog  and  use  it  in  his  measurements. 

What  is  usually  understood  by  him  as  the 
point  pf  the  frog  is  the  half-inch  blunt  point  B, 
in  the  diagram  below. 

It  is  true  it  is  a  point  of  the  frog,  but  it  is  the 
Actual  or  practical  point,  and  not  the  correct  or 


No.  7. 


theoretical  point,  which  should  be  used  by  him 
in  his  measurements. 

The  correct  point  is  the  intersection,  A,  of  the 
gauge  lines  of  the  two  sides  of  the  frog  forming 
the  angle,  and  it  is  several  inches  beyond  the 
half-inch  blunt  point,  according  to  the  number  of 
the  frog,  and  it  is  known  as  the  theoretical  point 
of  frog. 

(43) 


44  PRACTICAL  SWITCH  WORK. 

To  find  where  the  theoretical  point  is,  take  two 
2-foot  rules  or  two  straight-edges  about  2  inches 
wide  and  3  or  4  feet  long,  and  place  them  along 
the  gauge  line  of  each  side  of  the  frog  point, 
and  where  they  meet,  as  A,  is  the  theoretical 
point  which  should  be  used  in  all  measurements 
to  or  from  the  frog  point  for  leads  or  distance 
between  frog  points. 

The  practical  point,  B,  should  not  be  con- 
sidered as  being  the  point,  as  by  doing  so  dhv 
tances  too  great  may  be  obtained,  and,  conse- 
quently, the  frogs  not  being  in  their  proper 
position,  everything  depending  upon  them  wi*l 
be  likewise  affected. 

Too  much  stress  cannot  be  laid  upon  the  inr  - 
portance  of  this;  as,  for  example,  in  a  ladder 
track,  if  the  first  few  frogs  are  a  few  inches 
out  of  their  true  position  all  the  others  will  bo 
out  also;  and  in  a  cross-over,  or  where  exact 
work  may  be  necessary,  even  a  few  inches  may 
make  too  much  of  a  difference. 


A  FROG-BOARD. 

For  expeditious  and  accurate  switch  work  a 
frog-board  is  indispensable. 

It  is  simply  a  board  sawed  to  correspond  to 
the  frog  angle,  and  is  used  to  locate  frogs  prac- 
tically by  moving  or  shifting  it  along  the  rail 
until  the  proper  position  of  the  frog  is  obtained, 
lust  as  if  the  frog  itself  were  used  in  the  same 
manner. 

It  is  usually  made  of  dry  pine,  or  any  other 
Jight  wood,  about  i  inch  thick,  6  to  12  inches 
wide,  and  5  to  7  feet  long,  according  to  the 
>i?ngth  of  the  frog  from  point  to  heel. 

The  following  diagram  shows  a  frog-board  : — 


No.  8. 


And  in  the  following  table  are  the  dimen- 
necessary  for  marking  out  the  board. 


(45) 


46  PRACTICAL  SWITCH  WORK. 

TABLE  No.  13. 
FROG-BOARD  DIMENSIONS. 


Frog  No. 

Length 
AtoC. 

Width 
B  to  D. 

Frog  No. 

Length 
A  to  C. 

Width 
B  to  D. 

Ft      In. 

Inches. 

Ft.     In. 

Inches. 

4 

4       o 

12 

9 

6       0 

8 

5 

5       o 

12 

10 

5       o 

6 

6 

5       o 

IO 

II 

5       6 

6 

7 

5       3 

9 

12 

6      o 

6 

8 

6      o 

9 

15 

6      3 

5 

To  make,  say  a  No.  8  board,  draw  a  straight 
chalk  or  pencil  line,  A  to  C,  through  the  middle 
of  the  board,  and  measure  6  feet  (taken  fron. 
table  opposite  No.  8  frog)  from  A  to  C;  at  C 
and  at  right  angles  to  the  line  A  C  measure  4f 
inches  to  B  and  D  respectively,  4^  inches  be 
ing  one-half  of  9  inches,  the  width  B  to  D  as  ir 
the  table.  Make  a  line  from  A  to  B  and  also 
from  A  to  D,  and  saw  out  the  board  on  those 
lines  and  it  will  be  the  correct  angle. 

For  a  No.  10  board  th.e  length  from  the  point 
A  to  the  end  at  C  is  5  feet,  and  width  6  inches, 
or  3  inches  on  each  side  of  the  line,  or  a  total  of 
6  inches,  also  taken  from  the  table. 

If  a  board  longer  than  the  length  here  given 
is  desired,  the  lines  forming  the  sides  A  to  B 
and  A  to  D  can  be  extended  as  far  as  the  total 


A   FROG-BOARD.  47 

width  of  the  board  will  permit,  but  in  no  case 
will  it  be  necessary  to  have  one  longer  than 
about  8  feet. 

Mark  upon  each  board  clearly  the  frog  num- 
ber to  which  it  corresponds.  For  this  reason 
a  surfaced  board  is  to  be  preferred  if  it  can  be 
obtained. 

The  intelligent  use  of  the  frog-board,  a  ball  of 
twine  and  a  good  tape-line  will  be  found  to  be 
very  helpful  in  all  more  than  ordinary  switch 
work,  as  by  them  all  the  frog  points  can  be  lo- 
cated beforehand,  the  string  representing  the 
gauge  line  of  the  frog  rail,  and  no  changing  of 
frogs  to  improve  the  line  will  have  to  be  done 
as  the  work  is  in  progress;  as  not  infrequently  it 
happens  that  after  the  work  is  done  it  is  evident 
that  by  a  little  change  in  the  position  of  the 
frogs  an  improvement  could  have  been  made. 

Frogs  should  never  be  located  carelessly  or 
their  location  guessed  at.  Use  a  board  in  every 
case  of  uncertainty  or  difficulty. 


NUMBERS  TO  USE  AND  WHERE. 

The  proper  selections  of  frogs  suitable  to  the 
requirements  of  the  various  conditions  of  railroad 
service  is  important. 

It  may  be  necessary  in  sharp  siding  curves  to 
use  frogs  less  than  a  No.  6,  but  for  ordinary  con- 
ditions, if  it  can  be  avoided,  it  is  not  advisable 
to  use  even  so  low  a  number  as  No.  6. 

The  increased  size  and  weight  of  engines  is 
such  that  the  turnout  curve  of  a  No.  8  frog, 
about  9^  degrees,  is  as  sharp  a  curve  as  ought 
to  be  used  by  the  ordinary  road  engine. 

Freight  cars  and  engines  made  for  sharp  curva- 
ture can  go  around  curves  as  high  as  60  degrees 
easily,  but  as  cases  where  this  is  necessary  are 
rare,  so  far  as  possible,  the  limit  should  be  about 
10  degrees,  or  that  corresponding  to  the  curve  of 
a  No.  8  frog.  It  is,  of  course,  frequently  neces- 
sary to  exceed  this,  but  it  should  be  avoided,  if 
possible. 

The  kind  of  service  to  which  the  numbers 
most  generally  used  are  best  adapted  is  as  fol- 
lows : — 

No.  4  frog,  for  very  sharp  curves  by  very  small 

engines. 

(48) 


NUMBERS  TO   USE  AND   WHERE.  49 

No.  6  frog,  for  general  use  by  small  engines  or 
occasional  use  by  large  engines. 

No.  8  frog,  for  general  use  in  heavy  service  by 
V.irge  engines. 

No.  10  frogr  for  heavy  service  and  usual  speed 
to  20  miles  an  hour. 

No.  12  frog,  for  usual  speed  20  to  30  miles  an 
X  hour. 

No.  15  frog,  for  speed  of  30  to  40,  or  more, 
miles  an  hour. 

About  the  best  numbers  for  ordinary  service 
are  Nos.  8,  9,  and  10. 

A  No.  15  is  suitable  for  turning  out  at  high 
s'peed  from  one  track  to  another.  Anything 
Lig;her  in  number  than  a  15  or  20  is  neither 
necessary  nor  advisable. 

There  is  no  necessity  of  having  so  many  frogs 
of  different  numbers.  The  even  numbers,  viz., 
6,  8,  10,  12,  and  16,  are  sufficient  to  meet  all  the 
ifccuirements  of  any  service,  as  are  likewise  the 
i-dd  numbers  7,  9,  n,and  15.  Either  of  these 
groups  are  recommended. 

Half  numbers  are  unnecessary,  as  all  that  is 
c'btained  by  them  can  be  obtained  by  using  the 
nearest  whole  number,  either  by  slightly  changing 
tfce  position  of  the  frog  or  the  alignment  of  the 
curve  when  it  is  placed  in  the  track,  without  in 
the  least  impairing  the  efficiency  of  the  turnout, 
4 


JO  PRACTICAL  SWITCH  WORK. 

To  the  practice  of  adding  turnout  to  turnout 
without  any  consideration  of  the  future  require- 
ments or  good  alignment  of  the  tracks  for  th^ 
purpose  of  avoiding  a  little  extra  work,  may  be 
attributed  many  objectionable  combinations  of 
frogs  and  annoying  complications  in  switch  work, 
and  to  avoid  this  it  should  be  the  endeavor  to 
use  nothing  less  than  a  No.  6  or  a  No.  8,  and  f'» 
arrange  them  so  as  in  all  cases  to  preserve  3ym 
metry  and  uniformity. 


THE  GAUGE  AT  THE  FROG. 

The  proper  gauging  of  frogs  is  more  important 
than  it  is  generally  considered  to  be.  In  fact 
there  is  nothing  in  the  detail  of  track  work  more 
important,  so  far  as  safety  is  concerned.  The 
practice  of  leaving  the  gauge  a  little  wide  at  the 
frog  point  should  not  be  followed,  except  where 
the  turnout  curve  is  very  sharp,  or  the  turnout  is 
upon  a  sharp  main-track  curve,  the  gauge  of 
which  then  may  have  to  be  widened. 

When  it  is  necessary  to  widen  the  gauge  at  the 
frog,  the  guard-rail  distance  should  always  be  in- 
creased exactly  as  much  as  the  gauge  is  widened. 
If  the  guard-rail  distance  is  2  inches  and  if  the 
gauge  is  widened  %  inch,  then  the  guard-rail  dis- 
tance should  be  2j  inches  instead  of  2  inches. 
It  is  a  mistake  to  suppose  that  the  all-important 
thing  is  to  make  the  guard-rail  distance  exact, 
without  regard  to  whether  or  not  the  gauge  is 
exact. 

The  exact  guard-rail  distance  is  to  be  used 
only  when  the  gauge  is  exact,  as  the  important 
thing  is  the  distance  from  the  gauge  line  of  the 
frog  to  that  edge  or  side  of  the  guard  rail  with 
which  the  passing  wheel  comes  in  contact,  and 
(5D 


52  PRACTICAL  SWITCH  WORK. 

which  determines  the  distance  the  guard  rail 
should  be  from  the  main  rail.  This  distance  is 
always  equal  to  the  gauge  of.  the  track  less  the 
guard-rail  distance.  For  4  feet  9  inch  gauge  and 
2  inch  guard-rail  distance  it  is  4  feet  7  inches. 
Fcr  4  feet  &J  inch  gauge  and  if  inch  guard-rail 
distance,  it  is  4  feet  6|  inches. 


WIDENING  THE  GAUGE  OF  CURVES. 

It  is  not  necessary  to  widen  the  gauge  of  all 
curves  indiscriminately,  simply  because  some 
curves  above  a  certain  degree  may  require  it 
under  certain  conditions. 

The  difficulty  generally  is  to  keep  track  from 
becoming  tro  wide,  and  it  is  important  to  know 
when  and  to  what  extent  it  is  advisable  to  in- 
crease the  £iuge. 

For  example,  the  curvature  of  the  legs  of  a 
"Y"  is  generally  about  20  degrees,  and  it  may 
be  advisable  to  widen  the  gauge  £  inch,  or  4  feet 
9  inches  to  4  feet  9^  inches. 

But  if  only  4  feet  8£  inch  engines  or  cars  use 
such  a  curve,  then  4  feet  9  inches  should  not  be 
exceeded,  but  if  both  4  feet  8£  inch  and  4  feet  9 
inch  engines  or  cars  are  to  be  provided  for,  then  it 
is  allowable  to  increase  the  4  feet  8£  inch  gauge  to 
4  feet  9  J  inches. 

In  ordinary  curvature,  as  high  as  about  10  de- 
grees, the  4  feet  9  inch  gauge  requires  no  increase 
generally,  but  the  4  feet  S£  inch  gauge  may,  on 
account  of  cars  of  wider  gauge  using  it.  It  is 
necessary,  therefore,  in  widening,  to  be  governed 
(53) 


54 


PRACTICAL  SWITCH  WORK. 


by  the  necessity  of  providing  for  cars  other  than 
those  to  suit  the  gauge  of  the  road. 

The  4  feet  8^  inch  gauge  may,  therefore,  have 
to  be  widened  something  like  in  the  following 
table  :— 

TABLE  No.  14. 

WIDENING  THE  GAUGE  OF  CURVES. 


DEGREE  OF 
CURV.S. 

For  both  4  feet  8%  inch  and 
4  feet  9  inch  v\  heels. 

For  either  4  feet  8^  inch  01 
4  feet  9  inch  wheels  only. 

3 

yi  inch  wide. 

4 

X 

6 

X 

8 

u 

10 

% 

X  inch 

wide.  , 

12 

# 

X 

14       ' 

% 

H 

*- 

16 

% 

H 

18     £, 

I 

i 

20 

I 

'A 

30      :! 

I 

X 

m  * 

To  enable  a  sharp  curve  to  be  used  safely,  in 
addition  to  widening  the  gauge,  there  should^e 
little,  if  any,  elevation.  A  2O-degree  curye 
needs  no  elevation  if  the  speed  is  slow. 

When  it  is  necessary  to  widen  the  gauge  of 
a  turnout  curve  the  maximum  or  greatest  in- 
crease should  be  at  the  frog  point,  and  the  in- 
crease from  the  gauge  at  the  switch,  where  it  is 
neat,  to  the  frog;  where  it  is  widest,  should  be 


THE  GAUGE  OF  CURVES.  55 

made  gradually.  When  the  gauge  has  been  in- 
creased at  the  frog  point  the  guard  rail  should 
be  the  same  distance  from  the  frog  it  would  be 
if  the  gauge  were  exact,  the  guard-rail  distance 
increasing  as  much  as  the  gauge  is  widened. 
Divide  the  increase  in  the  gauge  by  two  or  four, 
and  make  the  gauge  correspondingly  wide  at 
'^ach  one-fourth  or  one-half  point  of  the  lead. 

Suppose  the  lead  is  48  feet  and  the  gauge  has 
?been  widened  -J  inch.  If  the  gauge  is  4  feet  9 
inches,  12  feet  from  the  switch  point  it  would 
be  4  feet  9^-  inches ;  at  24  feet  it  would  be  4  feet 
9^  inches;  at  36  feet,  4  feet  9!  inches;  and  at 
48  feet,  or  the  frog  point,  it  would  be  4  feet  9^ 
inches,  or  \  inch  wide. 

The  same  results  can  be  obtained  by  first 
gauging  the  track  accurately  and  then  placing 
the  guard  rail  the  required  distance  from  the 
main  rail,  and  this  is  the  way  it  is  generally  done ; 
but  when  the  gauge  is  widened  or  the  guard-rail 
distance  carelessly  measured,  the  effect  is  seen 
upon  the  frog  and  guard  rail.  Every  foreman 
should  be  provided  with  a  guard-rail  gauge,  not 
combined  with  but  separate  from  his  track  gauge, 
and  no  guard  rail  should  be  set  without  it. 

On  tangents  or  light  curves  there  should  be 
no  variation  whatever  from  the  exact  gauge  or 
/guard-rail  distance. 


56  PRACTICAL  SWITCH  WORK. 

A  frog  upon  the  high  side  of  a  curve  may 
cause  a  noticeable  lurch  to  the  passing  train  when 
in  exact  gauge  and  having  the  guard-rail  distance 
exact,  if  the  remainder  of  the  curve  is  wide  as 
to  gauge,  either  made  so  or  has  become  so  from 
its  natural  tendency  to  widen.  In  such  a  case  it 
might  be  well  to  make  the  gauge  at  the  frog  the 
same  as  that  of  the  curve,  but  the  guard  rail 
"should  always  be  the  same  distance  from  the 
frog  whether  the  gauge  is  exact  or  wide. 

When  a  frog  is  upon  the  low  side  of  a  curve 
the  gauge  should  be  kept  as  nearly  exact  as  pos- 
sible by  rail  braces  upon  the  high  side  opposite 
the  frog,  and  the  changes  in  the  gauge  from  be- 
ing exact  at  the  frog  to  what  the  curve  may  have 
become  wide  should  be  made  gradually  upon 
each  side  of  the  frog.  In  this  case  the  wing 
rail  of  the  frog  acts  as  a  guard  rail  upon  the  low 
side,  and  the  wider  the  gauge  the  greater  the? 
blow  and  injury  to  the  frog  and  liability  to  acci- 
dent. 

To  gauge  a  frog  properly  the  gauge  should  be 
placed  at  the  heel  and  toe  and  the  frog  tacked  at 
neat  gauge,  that  is,  held  in  position  by  the  spikes 
about  half  driven;  then  bring  the  frog  to  neat 
gauge  at  a  point  from  six  to  twelve  inches  back 
of  the  blunt  point,  where  there  is  no  bevel.  The 
beveled  point  really  makes  the  gauge  a  little 


\VJDENING    THE  GAUGE  OF  CtJRVES*  ^ 

wide  where  it  may  be  needed  to  be  so,  so  there 
is  no  necessity  of  increasing  it  upon  straight 
line.  All  gauging  should  be  done  so  that  the 
gauge  will  fall  into  place  easily  and  fit  neatly. 

The  distance  between  the  wing  rail  and  the 
point  or  tongue  of  the  frog,  also  at  the  point  be- 
tween the  frog  point  and  toe,  where  the  two  wing 
rails  are  closest,  is  usually  the  same  as  the  guard- 
rail distance. 

The  two  guard-rail  distances  most  generally 
used  are  2  inches  for  4  feet  9  inch  gauge  and  if 
inches  for  4  feet  8|-  inch  gauge. 

Some  of  the  evidences  of  improper  gauging 
are : — 

1.  When    the  guard  rail  or  the  wing  rail  of 
the  frog  is  unnaturally  worn  by  the  flange  and 
difficult  to  be  kept  in  position,  making  many  rail 
braces  necessary. 

2.  When  near  the  end  of  the  guard  rail  there 
is  an  abrupt  change  from  a  badly  worn  rail  head 
to  a  full  head  through  the  guard  rail  upon  the 
high  side  of  the  curve. 

3.  When  there  is  a  similar  mark  at   either 
end  of  the  frog  when  it  is  upon  the  high  side  of 
the  curve. 

4.  When  the  frog  receives  a  blow  from  the 
passing  wheel  or  shows  evidence  of  unnatural 
strain  by  pulling  apart. 


5  PRACTICAL  SWITCH  WORK. 

Whenever  these  evidences  are  found,  the  gaug- 
ing should  at  once  be  gone  over  and  corrected. 

Additional  guard-rail  chairs  or  rail  braces  are 
not  infrequently  used  to  remedy  the  difficulties 
just  mentioned,  but  the  necessity  for  frogs  and 
guard  rails  to  be  supported  so  fully  is  an  evidence 
of  ignorance  as  to  the  real  cause  of  the  trouble. 

Guard  rails  cannot  easily  be  kept  to  the  exact 
guard-rail  distance,  but  when  they  exceed  by  \ 
of  an  inch  the  required  distance,  they  should  be 
taken  up  and  relaid.  Whenever  a  reasonable 
number  of  guard-rail  chairs  art  not  sufficient  to 
hold  the  frog  or  guard  rai  I  in  \>oSticn,  there  is 
something  wrong  with  the  pu^v^  an  { it  should 
be  attended  to  promptly. 


TO  LINE  TURNOUT  CURVES. 

It  is  the  almost  uniform  practice  to  line  the 
turnout  curve,  called  "lining  the  lead,"  entirely 
by  the  eye ;  and  although  it  can  be  done  in  that 
vvay  very  well,  there  is,  however,  a  way  by  which 
the  curvature  of  the  turnout  can  be  obtained 
more  rapidly  and  accurately  than  is  obtained  by 
the  eye  alone.  This  method  is  that  of  locating 
by  ordinates  two  or  three  points  of  the  turnout 
rurve,  as  shown  in  the  diagram  below. 


No.  9. 


In  this  diagram,  A  is  the  theoretical  point  of 
frog,  and  C  is  the  point  or  beginning  of  the 
theoretical  curve,  not  always  the  point  of  the 
switch,  as  might  be  supposed.  What  is  wanted 
by  the  trackman  is  the  correct  alignment  or  line 
of  the  curve  from  A  to  C,  or  from  the  frog  point 
to  the  switch. 

(59) 


6O  PRACTICAL  SWITCH  WORK. 

The  straight  line  between  A  and  C  is  called 
the  chord,  and  the  distances  from  it  to  the  curve 
at  D,  E,  and  F  are  called  ordinates.  By  measur- 
ing from  the  frog  point  A  along  the  chord  a 
certain  distance  to  D,  E,  and  F  respectively,  and 
from  these  points  at  right  angles,  by  measuring 
certain  other  distances  to  the  curve,  all  of  which 
are  given  in  the  Tables  Nos.  15,  16,  and  17, 
three  points  of  the  turnout  curve  may  be  located, 
and  having,  in  addition,  the  point  of  frog  and 
point  of  switch  already  located,  all  that  is  neces- 
sary to  be  done  is  to  line  between  these  points 
to  obtain  the  correct  alignment  of  the  curve. 

When  any  lining  of  this  kind  is  to  be  done, 
having  decided  upon  the  location  of  the  frog, 
the  first  thing  to  do  is  to  locate  the  point  of  the 
turnout  curve  C.  This  may  be  done  by  measur- 
ing the  theoretical  lead  from  A  to  B,  C  being 
directly  opposite  B,  upon  the  other  rail.  Make' 
a  chalk-mark  at  C,  the  beginning  of  the  curve, 
and  stretch  a  string  from  A,  the  theoretical  point 
of  the  frog,  to  C,  the  point  of  the  curve,  not  the 
point  of  the  switch,  unless  the  frog  has  the  full 
theoretical  lead.  The  string  corresponds  to  the 
line  from  A  to  C,  and  the  offsets  from  this  line 
to  the  curve  are  the  ordinates. 

The  ordinates  at  D  and  F  are  called  quarter 
ordinates  because  they  are  each  at  a  point  one- 


TO  LINE   TURNOUT  CURVES.  1 

fourth  the  distance  from  the  point  of  the  frog  to 
the  point  of  the  theoretical  curve  at  C. 

The  ordinate  at  E  is  called  the  "  middle  ordi- 
nate"  because  it  is  midway  between  the  point 
of  the  frog  and,  the  point  of  the  curve  at  C 

The  middle  ordinate  is  equal  to  one-fourth 
the  gauge  for  No.  5  frogs  and  over,  and  when 
the  gauge  does  not  vary  far  from  4  feet  9  inches. 

For  4  feet  8£  inch  gauge  it  is,  therefore,  I  foot 
2£  inches,  and  for  4  feet  9  inches  it  is  I  foot  2j 
inches. 

The  quarter  ordinates  are  T3¥  the  gauge,  or 
i  of  inches  for  4  feet  8^  inch  and  lof  inches  for 
4.  feet  9  inch  gauges. 

The  full  theoretical  lead,  as  given  in  the  ta- 
bles, should  always  be  used  to  find,  by  measure- 
ment, the  point  of  curve  at  C,  even  if  the  lead 
is  shortened. 

The  following  tables  give  the  distance  or  lead 
to  be  measured  from  the  frog  point  to  find  the 
point  of  curve.  They  give  also  the  middle  and 
quarter  ordinates  at  the  proper  distance  from 
the  frog  point  for  different  frogs  and  gauges :— 


62 


PRACTICAL  SWITCH  WORK. 


TABLE   No.  15. 
FOR  4  FEET  SX  INCH  GAUGE. 


FROG  POINT  TO  ORDINATES. 

FROG 
No. 

THEORETI- 
CAL LEAD. 

DIAGONAL 
DISTANCE, 
ATOC. 

Quarter, 

Middle, 

lo^i  Inches. 

r  Ft.  2*4  In. 

Ft.       In. 

Feet.  Inches. 

Feet.  Inches. 

Feet.  Inches. 

4 

37      8 

9        6 

19        o 

38        o 

5 

47       i 

II          10 

23        8 

47        4 

6 

56      6 

H        5 

28      10 

56        8 

7 

65     ii 

16        6 

33        o 

66        i 

8 

75      4 

18       ii 

37        9 

75        6 

9 

84      9 

21        3 

42        5 

84      ii 

10 

94      2 

23        7 

47        2 

94        4 

ii 

103      7 

25       ii 

51       10 

103        8 

12 

113      o 

28        3 

56        7 

113        i 

15 

I4i       3 

35        4 

70        8 

141         4 

Note  that  i  foot  2\  inches  is  the  middle  ordi  - 
nate  and  lof  inches  is  for  both  quarter  ordinates. 
Measurement  always  to  be  taken  from  the 
theoretical  point  of  the  frog,  along  the  string  to 
the  point  where  the  ordinate  is  measured. 


TO  LINE   TURNOUT  CURVES. 


TABLE   No.  16. 
FOR  4  FEET  9  INCH  GAUGE. 


'  "  v  -i 

FROG  POINT  TO  ORDINATES. 

FROG 
No. 

THEORETI- 
CAL LEAD. 

DIAGONAL 
DISTANCE, 
A  ToC. 

Quarter, 

Middle, 

10^  Inches. 

i  Ft.  2#  In. 

Ft.       In. 

Feet.  Inches. 

Feet.  Inches. 

Feet.  Inches. 

4 

38        0 

9          7 

19           2 

38        4 

5 

47       6 

II        11 

23      10 

47        9 

6 

57       o 

14        4 

28        7 

57        2 

7 

66       6 

16        8 

33        4 

66        8 

8 

76       o 

19        o 

38        i 

76        '2 

9 

85       7 

21        5 

42       10 

85        9 

10 

95       o 

23        9 

47        7 

95        i 

ii 

104       6 

26            2 

52        4 

104        7 

12 

114       o 

28        6 

57        o 

114        i 

15 

142       6 

35        8 

7i        4 

142         7 

Note  that  i  foot  2^  inches  is  the  middle  ordi- 
nate  and  iof  inches  is  for  both  quarter  ordinates. 
Measurement  to  be  taken  from  the  theoretical 
point  of  the  frog,  along  the  string  to  the  point 
where  the  ordinate  is  measured. 


PRACTICAL  SWITCH  WORK. 


TABLE  No.  17. 
FOR  3  FEET  GAUGE. 


FROG  No. 

THEORETI- 
CAL LEAD. 

FROG  POINT  TO  ORDINATES. 

DIAGONAL 
DISTANCE, 
A  TO  C 

Quarter,  6^  In. 

Middle,  9  In. 

Feet.  Inches. 

Feet.    Inches. 

Feet.    In  hes. 

Feet.  Inches 

4 

24       o 

6        o 

12 

24         2 

5 

30       o 

7        6 

1^ 

30          2 

6 

36       o 

9        o 

18 

36          2 

7 

42       o 

10        6 

21 

42          I 

8 

48       o 

12           O 

24 

48          I 

9 

54       o 

13        6 

27        o 

54       i 

10 

60       o 

15           0 

30        o 

60       i 

Note  that  9  inches  is  the  middle  ordinate  and 
6f  inches  is  for  both  quarter  ordinates.  Measure- 
ment always  to  be  taken  from  the  theoretical 
point  of  the  frog. 

To  explain  the  use  of  these  tables,  suppose 
it  is  desired  to  line  the  turnout  curve  of  a  No. 
8  frog,  4  feet  9  inch  gauge.  Refer  to  Table 
No.  1 6,  and  in  column  giving  theoretical  lead 
of  a  No.  8  frog,  76  feet  is  found.  Measure 
the  lead  A  to  B,  76  feet  from  the  point  of 
frog  in  the, direction  of  the  switch,  and  on  the 
gauge  of  the  rail  at  C,  exactly  opposite  B,  make 
a  chalk-mark.  The  diagonal  distance  A  to  C, 
taken  from  the  last  column,  may  be  measured 
to  C,  if  there  is  at  hand  a  tape-Une  long  enough* 


TO  LINE   TURNOUT  CURVES.  65 

Stretch  a  line  from  point  of  frog  to  the  chalk- 
mark  at  C,  which  is  the  point  of  the  curve. 
This  string  is  the  line  from  which  the  ordinates 
are  to  be  measured. 

Refer  again  to  table  No.  16,  and  in  the  third 
column,  opposite  No.  8  frog,  19  feet  is  found  to 
be  the  distance  from  the  frog  point  to  where  the 
first  quarter  ordinate  is  measured.  Measure 
along  the  line  19  feet  from  the  frog  point,  and 
at  this  point  bring  the  gauge  of  the  rail  of  the 
turnout  curve  to  lof  inches  from  the  string  and 
tack  it  with  spikes. 

Refer  again  to  the  table,  and  find  that  the 
middle  ordinate  is  at  38  feet  i  inch  from  the 
fi.v>g  point.  Continue  the  measurement  38  feet 
\  inch  from  the  frog  point,  and  bring  the  gauge 
of  the  rail  to  i  foot  2j  inches  from  the  string 
and  tack  it.  Two  points  of  the  curve,  one  at 
the  middle  and  the  other  at  the  quarter  ordinate, 
are  thus  established. 

With  the  point  of  switch,  point  of  frog,  and 
these  two  points  all  located,  all  that  is  necessary 
to  be  done  to  finish  is  to  line  between  all  the 
points  with  the  eye,  and  the  correct  curvature  is 
obtained. 

If  the  distance  from  the  frog  places  the  sec- 
ond quarter  ordinate,  at  F,  upon  a  split  switch  or 
slide  rail  of  a  stub  switch,  this  ordinate  may  be 
5 


66  PRACTICAL  SWITCH  WORK. 

omitted,  as  the  heel  of  the  split  switch  or  the 
head-block  of  the  stub  switch  locates  its  posi- 
tion with  reference  to  the  turnout  curve. 

The  diagonal  distance  in  the  last  column  of 
the  tables  is  the  distance  in  a  straight  line  from 
the  point  of  frog  to  the  point,  C,  of  the  theoret- 
ical curve.  By  using  it  and  measuring  with  a 
loo-foot  tape-line  the  point  of  the  curve  can  be 
found,  perhaps,  more  easily  than  by  measuring 
the  lead,  but  having  only  a  5o-foot  tape-line  the 
easiest  way  is  to  measure  the  lead  and  movo 
over  to  the  opposite  rail,  as  directed. 


THE  LINE  AT  THE  HEEL  OF  THE 
FROG. 

In  lining  the  curve  at  the  heel  of  the  frog  in  a 
turnout  when  it  reverses  into  a  parallel  track,  a 
very  common  mistake  is  made  in  beginning  the 
curve  at  the  frog  point.  The  supposition  is,  and 
it  is  true,  that  the  curvature  at  tl^e  heel  of  the 
frog  should  be  the  same  as  that  between  the 
frog  and  the  switch,  and  yet  in  lining,  notwith- 
standing the  greatest  care  may  be  exercised,  a 
good  curve  cannot  be  obtained.  The  reason  is 
this :  A  single  turnout  is  equivalent  to  a  cross- 
over between  two  parallel  tracks.  In  the  latter 
there  should  be  straight  line  between  the  frog 
points.  There  should,  likewise,  be  straight  line 
from  the  point  of  the  frog  in  a  turnout  for  the 
distance  the  same  frogs  would  be  apart  in  a 
cross-over. 

The  distance  the  line  should  be  straight  is 
given  in  the  following  table  for  4  feet  8£  inch 
and  4  feet  9  inch  gauges : — 


(67) 


68 


PRACTICAL  SWITCH  WORK. 


TABLE  No.  18. 
LENGTH  OF  TANGENT  AT  HEEL  OF  FROG. 


FROG  No. 

DISTANCE  BETWEEN  TRACKS. 

6  Feet  6  Inches. 

7  Feet. 

7  Feet  6  Inches. 

Feet. 

Inches. 

Feet.    Inches. 

Feet. 

Inches. 

6 

IO 

6 

13 

6             16 

6 

7 

12 

3 

15 

9             19 

3 

8 

14 

o             18 

0                  22 

0 

9 

15 

9             20 

3 

24 

9 

10 

17 

6 

22 

6 

27 

6 

ii 

19 

3 

24 

9 

30 

3 

12 

2! 

o 

27 

0 

33 

o 

15 

26 

3 

33 

9 

3 

At  a  point  about  50  feet  back  of  the  frog,  first 
measure  the  distance  between  the  tracks  which 
are  connected  by  the  turnout,  and  refer  to  the 
table  above,  and  in  the  column  under  the  dis- 
tance nearest  that  obtained  by  measurement,  and 
opposite  the  number  of  the  frog  that  is  in  the 
turnout,  is  found  the  length  of  the  straight  line. 
If,  for  example,  the  frog  is  No.  8  and  the  dis- 
tance between  tracks  7  feet  6  inches,  the  straight 
line  or  tangent  is  22  feet.  Make  it  straight  for 
22  feet  and  from  there  curve  for  a  distance 
equal  to  the  lead  of  about  9^  times  the  frog 
number,  which,  in  this  case,  would  be  76  feet. 
This  curve  will  be  the  same,  practically,  as  that 
at  the  toe  of  the  frog  and  its  length  equal  to 
that  of  the  theoretical  lead, 


THE  LINE  AT   THE  HEEL    OF   THE  fROG.          69 

It  is  not  necessary  to  have  the  exact  distance 
between  the  tracks.  Those  in  the  table  are 
near  enough.  Nor  is  it  necessary  to  have  more 
than  a  reasonable  length  of  straight  line  at  the 
heel  of  the  frog,  keeping  somewhat  near  the 
distances  in  the  table. 


CROSS-OVERS  UPON  STRAIGHT 
LINE. 

A  through  crossing  or  cross-over  is  made  up  of 
two  single  turnouts  facing  in  opposite  directions 
and  connected  between  the  frogs  by  a  piece  of 
straight  track.  What  is  true  of  the  turnout  in 
regard  to  the  lead,  &c.,  is  true  also  of  those 
forming  the  cross-over,  the  only  thing  in  anywise 
difficult  being  to  connect  them,  that  is,  to  find 
the  position  of  the  second  frog.  This  can  be 
done  in  various  ways,  theoretically  or  practi- 
cally, with  equally  satisfactory  results  generally. 

In  ordinary  cross-overs  between  straight  and 
parallel  tracks  the  line  between  the  frog  points 
should  always  be  straight,  unless  the  distance 
between  the  tracks  is  so  great  that  it  is  advisable 
to  save  distance  by  reversing  at  a  point  midway 
between  the  frog  points. 

But  for  the  usual  distance  of  seven  or  eight 
feet  which  tracks  are  apart  in  general  railroad 
operation,  there  should  always  be  straight  line 
between  the  frogs. 

The  distance  between  tracks  should  not  be 
(7o) 


CROSS-OVERS   UPON  STRAIGHT  LINE.  J\ 

/ess  than  will  permit  a  man  to  walk  erect  and 
comfortably  between  cars  standing  upon  them. 
Seven  feet  between  the  outside  of  the  rails,  or 
about  7  feet  6  inches  between  the  gauge  lines,  is 
sufficient  to  do  this,  and,  so  far  as  possible,  any- 
thing less  should  be  avoided  in  laying  new 
tracks  or  renewing  old  ones. 

Parallel  tracks  should  also  be  a  uniform  dis- 
tance apart,  whatever  distance  may  be  consid- 
ered to  be  best ;  and  work  upon  tracks  not  so 
should  be  done  with  a  view  to  their  all  being 
thrown  eventually  to  a  uniform  and  sufficient 
distance  apart. 

Trackmen  are  accustomed  to  consider  the  dis- 
tance between  tracks  as  being  between  the  out- 
side of  the  rail  heads,  and  to  measure  between 
them  for  the  distance  apart.  This  should  not 
be  done.  The  distance  between  the  gauge  lines, 
that  is,  between  the  inside  or  gauge  side  of  the 
rails,  should  always  be  taken  as  the  distance  be- 
tween tracks,  for  the  reason  that  the  gauge  line 
or  inside,  not  the  outside,  of  rail  head,  is  the  basis 
of  measurement  in  all  switch  and  track  work,  or 
should  be. 

The  foreman  who  has  set  frogs  by  measure- 
ment, and  has  not  been  satisfied  with  them, 
might  have  found  that  his  lack  of  success  was 
largely  due  to  his  not  having  taken  the  distance 


72  PRACTICAL  SWITCH  WORK. 

between  gauge  lines,  it  being  a  very  common 
error  not  to  do  so. 

The  work  of  putting  in  a  cross-over  should  be 
proceeded  with  in  the  same  manner  as  that  of 
putting  in  a  single  turnout.  The  location  of 
either  the  frog  point  or  head-block  should  first  be 
decided  upon,  and  no  work  should  be  done  until 
the  location  of  both  head-blocks  and  both  frog- 
points  have  been  made  and  clearly  marked  upon 
the  rails,  either  accurately  or  approximately. 

In  deciding  upon  the  location  of  the  point  of 
the  first  frog,  so  far  as  possible  it  should  be  the 
endeavor  to  place  the  heel  or  toe  of  the  frog  at 
a  joint  to  avoid  making  a  cut,  unless  the  joints 
at  the  head-block,  particularly  in  the  case  of  a 
point  or  split  switch,  are  so  disposed  as  to  make 
it  better  to  first  locate  the  point  of  the  switch, 
in  which  event  the  location  of  the  frog  point  will 
have  to  be  determined  by  measurement,  regard- 
less of  the  joints.  Having  located  either  the 
point  of  the  switch  or  the  frog  point,  the  other 
may  be  found  as  directed  on  pages  8-12. 

When  the  location  of  the  first  frog  has  been 
made,  and  it  is  not  particular  which  of  the  two 
is  made  first,  the  point  of  the  second,  or  the  one 
in  the  other  parallel  track,  will  be  a  distance 
from  the  point  of  the  first  frog,  measured  along 
the  straight  or  parallel  track,  varying  according 


CROSS-OVERS  UPON  STRAIGHT  LINE. 


73 


to  the  frog  number  and  the  distance  the  tracks 
are  apart.  What  this  distance  between  the  frog 
points  is  may  be  found  approximately  in  every 
case  by  the  following  rule  : — 

From  the  distance  between  gauge  lines  of  the 
parallel  tracks  subtract  the  gauge  of  the  track 
and  multiply  the  remainder  by  the  number  of 
the  frog,  and  it  will  give  the  distance  between 
the  frog  points  measured  along  the  parallel  tracks, 
as  C  to  B  in  the  diagram. 


Wo.  10. 

Suppose  the  distance  between  the  gauge  lines 
is  7  feet  5  inches,  the  gauge  4  feet  9  inches,  and 
the  frog  a  No.  8.  The  difference  between  7  feet 
5  inches  and  4  feet  9  inches  is  2  feet  8  inches. 
Multiplying  2  feet  8  inches,  or  32  inches,  by  8, 
we  have  256  inches,  equal  to  21  feet  4  inches. 
Measure  this  distance  along  the  rail  opposite  the 
frog,  from  C  to  B,  in  Diagram  No.  10,  which  is 
exactly  opposite  the  point  of  the  frog  A.  Place 
the  point  of  the  second  frog  at  A.  Suppose  the 
distance  between  tracks  is  7  feet,  gauge  4  feet 


74  PRACTICAL  SWITCH  WORK. 

SJ  inches,  and  frog  a  No.  9.  The  distance  from 
C  to  B  would  then  be  20  feet  7  inches,  obtained 
by  the  same  process. 

In  the  following  tables  are  given  the  distances 
obtained  by  the  rule  just  given,  for  4  feet  8^ 
inch  and  4  feet  9  inch  gauges,  for  every  3 
inches  variation  in  the  distance  between  gauge 
lines  from  6  feet  6  inches  to  8  feet.  For  any 
other  distances  the  tracks  are  apart,  the  distance 
C  to  B  can  be  obtained  by  the  same  rule. 

TABLE  No.  19. 

DISTANCE  BETWEEN  FROG  POINTS,  MEASURED  ALONG 
THE  PARALLEL  TRACK. 

Gauge,  4  feet  8^  inches. 


d 
K 

DISTANCE  BETWEEN  GAUGE  LINES. 

\ 

fe 

6ft.6in. 

6  ft.  9  in. 

7  ft.  o  in. 

7  ft.  3  in. 

7  ft.  5  in 

7  ft.  6  in. 

7  ft.  9  in. 

8ft.  oin. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

10  9 

12  3 

13  9 

15  3 

16  3 

16  9 

18  3 

19  9 

7 

12  6 

*4  3 

16  o 

17  9 

19  o 

19  6 

21   3 

23  o 

8 

14  4 

16  4 

18  4 

20  4 

21   8 

22   4 

24  4 

26  4 

9 

16  I 

18  4 

20  7 

22  10 

24  5 

25   I 

27  4 

29  7 

10 

17  ii 

20  5 

22  II 

25   5 

27  i 

27  II 

30  5 

32  ii 

ii 

19  8 

22  5 

25   2 

27  II 

29  10 

30  8 

33  5 

36  2 

12 

21   6 

24  6 

27  6 

30  6 

32  6 

33  6 

36  6 

39  6 

15 

26  10 

30  7 

34  4 

38  I 

40  8 

41  10 

45  7 

49  4 

UPON  STRAIGHT  LINE.  75 

TABLE  No.  20. 
Gauge,  4  feet  9  inches. 


0 

DISTANCE  BETWEEN  GAUGE  LINES. 

0 

tf 

6  ft.  6  in. 

6  ft.  9  in. 

7  ft.  o  in. 

7  ft.  3  in.  7  ft.  5  in.  7  ft.  6  in.  7  ft.  9  in. 

8  ft.  o  in. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

10  6 

12  0 

13  6 

15   0 

16  o 

16  6 

18  o 

19  6 

7 

12  3 

14  o 

15  9 

17  6 

18  8 

19  3 

21   0 

22  9 

8 

14  o 

16  o 

18  o 

20   0 

21  4 

22   0 

24  o 

26  o 

Q 

15  9 

18  o 

20  3 

22   6 

24  o 

24  9 

27  o 

29  3 

10 

17  6 

2O   0 

22   6 

25  o 

26  8 

27  6 

30  o 

32  6 

II 

19  3 

22  0 

24  9 

27  6 

29  4 

30  3 

33  o 

35  9 

12 

21   O 

24  o 

27  o 

30  o 

32  o 

33  o 

36  o 

39  o 

15 

26  3 

30  o 

33  9 

37  6 

40  o 

4i  3 

45  o 

48  9 

The  distances  in  these  tables,  obtained  by  the 
rule  given  *on  page  73,  are  not  exactly  correct, 
but  they  can  be  used  with  excellent  results,  from 
the  fact  that  the  difference  of  a  few  inches  does 
not  seriously  affect  the  line  through  the  frogs. 

There  is  no  such  simple  rule  by  which  the  ex- 
act distance  between  frog  points,  measured  along 
the  parallel  track,  can  be  obtained.  In  Tables 
Nos.  21  and  22,  however,  are  given  the  correct 
distances  between  the  frogs,  which,  upon  com- 
parison, will  be  found  to  differ  but  slightly  from 
those  in  Tables  Nos.  19  and  20.  The  choice  of 
these  tables  is  left  to  the  foreman,  the  prefer- 
ence, however,  being  in  favor  of  those  giving  the 
correct  distances. 


PRACTICAL   SWITCH  WORK. 


TABLE  No.  21. 

GIVING  CORRECT  DISTANCES  BETWEEN  FROG  POINTS, 

MEASURED  ALONG  PARALLEL  TRACK. 

Gauge,  4  feet  8^  inches. 


6 

DISTANCE  BETWEEN  GAUGE  LINES. 

0 

£ 

6  ft.  6  in. 

6ft.  pin. 

7  ft.  o  in.  7  ft.  3  in. 

7  ft.  5  in. 

7  ft.  6  in. 

7  ft.  9  in. 

8  ft.  o  in. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

10  3 

ri  9 

13  3 

14  9 

15  9 

16  3 

17  9 

!9  3 

7 

12   2' 

13  II 

15  8 

17  4 

18  6 

19  I 

20  10 

22   7 

8 

14  o 

16  o 

18  o 

20   0 

21  4 

22   0 

23  II 

25  II 

9 

15  10 

18  i 

20  4 

22   7 

24  o 

24  9 

27  o 

29  3 

10 

17  8 

2O   2 

22   8 

25   I 

26  9 

27  7 

30  I 

32  7 

ii 

19  6 

22   2 

24  II 

27  8 

29  6 

30  5 

32   2 

35  ii 

12 

21  3 

24  3 

27  3 

30  3 

32  3 

33  3 

36  3 

39  3 

15 

26  8 

30  5 

34  2 

37  ii 

40  5 

41  8 

45  5 

49  2 

TABLE  No.  22. 
Gauge,  4  feet  9  inches. 


DISTANCE  BETWEEN  GAUGE  LINES. 


i 

6ft.6in. 

6  ft.  9  in. 

7  ft.  o  in. 

7ft.  3in. 

7  ft.  5  in. 

7  ft.  6  in. 

7  ft.  9  in. 

8  ft.  o  in. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

10  0 

II   6  13  O 

14  6 

15  6 

16  o 

17  6 

19  o 

7 

II  IO 

13  7 

15  4 

17   I 

'8  3 

18  10 

20   6 

22  4 

8 

13  8 

15  8 

17  8 

19  8 

21   0 

21   8 

23  7 

25  7 

9 

15  5 

17  8 

19  II 

22   2 

23  8 

24  5 

26  8 

28  ii 

10 

17  3 

19  9 

22   3 

24  8 

26  4 

27   2 

29  8 

32  2 

ii 

19  o 

21  9 

24  6 

27  3 

29  i 

30  o 

32  9 

35  6 

12 

20  9 

23  9 

26  9 

29  9 

3i  9 

32  9 

35  9 

38  9 

15 

26  o 

29  10  33  6 

37  4 

39  10 

41  o 

44  9 

48  6 

CROSS-OVERS  UPON  STRAIGHT  LINE.  JJ 

Tr  use  all  these  tables,  first  measure  very  care- 
full}7  the  distance  between  the  gauge  lines  of  the 
tracks  in  which  the  cross-over  is  to  be  placed, 
which,  for  example,  will  be  supposed  to  be  7 
feet  5  inches,  .the  frogs  being  No.  8  and  the 
gauge  4  feet  9  inches.  In  Table  No.  22,  look  in 
the  column  under  7  feet  5  inches  and  opposite 
No.  8,  and  find  21  feet  o  inch.  This  is  the  cor- 
rect distance  between  the  frog  points  along  the 
straight  rail  C  to  B,  page  73.  Thejiistance  ob- 
tained by  the  rule,  and  found  in  Table  No.  20, 
is  21  feet  4  inches. 

Should  the  distance  between  gauge  lines  be 
one  not  given  in  the  tables,  for  example,  6 
ieet  10  inches,  and  if  the  track  cannot  be  thrown 
to  6  feet  9  inches  or  7  feet,  then  obtain  the  dis- 
tance by  the  rule  on  page  73,  in  the  manner  al- 
ready explained ;  or  take  the  difference  between 
the  distance  for  7  feet  and  that  for  6  feet  9 
inches  and  divide  it  by  3,  and  add  one-third  or 
two-thirds  of  the  difference  to  6  feet  9  inches,  ac- 
cording as  the  increase  in  the  distance  apart  is  i 
or  2  inches. 

Another  and  easy  way  to  ascertain  the  location 
of  the  point  of  the  second  frog  is  to  know  what 
the  distance  is  in  a  straight  line  between  the  frog 
points.  This  distance  we  will  call  the  diagonal 
distance,  and  is  from  A  to  B  in  Diagram  No,  i  j. 


78  PRACTICAL  SWITCH  WORK. 

Suppose  a  crossing  is  to  be  put  in  between 
two  straight  and  parallel  tracks,  as  shown  in  the 
diagram,  and  that  the  location  of  the  point  of 
the  first  frog,  at  A,  has  been  decided  upon.  If 
the  diagonal  distance  between  the  frog  points 
for  any  frog  is  given  for  certain  distances  be- 
tween tracks,  then  a  simple  measurement  of  this 
distance  from  the  point  of  one  frog  will  deter- 
mine where  the  point  of  the  other  should  be. 

From  Table  No.  24  we  find  that  for  7  feet  5 
inches  between  gauge  lines,  No.  8  frogs  and  4 


No.  11. 

feet  9  inch  gauge,  the  distance  between  frog 
points  is  22  feet  3  inches.  From  the  theoretical 
point  of  frog,  if  it  is  already  in  the  track,  or 
from  a  chalk-mark  upon  the  gauge  line  of  the 
rail  where  it  is  to  be,  if  it  is  not,  measure  22 
feet  3  inches  in  a  direction  from  A  to  B,  and 
where  this  distance  meets  or  intersects  the 
gauge  line  of  the  opposite  rail  will  be  the  point 
of  the  other  frog.  Mark  it  with  chalk  or  a  rail- 
cutter,  and  place  the  frog  there. 


CROSS-OVERS  UPON  STRAIGHT  LINE. 


The  location  of  the  point  of  the  frog  found  in 
this  manner  should  be  the  same  as  that  obtained 
by  measurement  of  the  distance  in  Table  No. 
22,  and  if  done  accurately  will  be  correct. 

The  following  tables  give  the  diagonal  dis- 
tance between  the  frog  points  :  — 

TABLE  No.  23. 

DIAGONAL  DISTANCE  BETWEEN  FROG  POINTS. 
Gauge,  4  feet  S>£  inches. 


i 

DISTANCE  BETWEEN  GAUGE  LINES  OF  TRACKS. 

| 

6  ft.  6  in.  6  ft.  9  in. 

7  ft.  o  in. 

7ft.3»». 

7  ft.  5  in. 

7  ft.  6  in. 

7  ft.  9  in. 

8  ft.  o  in. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

12   I 

13  7 

15  0 

16  5 

17   5 

17  II 

19  4 

20  10 

7 

13  9 

15  5 

17   2 

18  10 

20   0 

20  6 

22   3 

24  o 

8 

'5  5 

17  4 

19  3 

21  3 

22   6 

23  3 

25   2 

27   2 

9 

17  i 

19  3 

21   6 

23  9 

25   I 

25  ii 

28 

3°  4 

10 

18  9 

21  3 

23  9 

26  i 

27   9 

28  7 

31 

33  7> 

ii 

20  6 

23   2 

25  JO 

28  7 

30  5 

3i  4 

33 

36  10 

12 

22   3 

25   2 

28   2 

3i  i 

33  i 

34  i 

37 

40  i 

15 

27  6 

31   2 

34  ii 

38  7 

41  i 

42  4 

46 

49  10- 

8O  'PRACTICAL  SWITCH  WORK. 

TABLE  No.  24. 
Gauge,  4  feet  9  inches. 

DISTANCE  BETWEEN  GAUGE  LINES  OF  TRACKS. 


6  I  i    '  I  i  I  i 

6ft. 6in.  6ft.9in  yft.oin.  yft.ain.  yft.sin.  7ft.6in.  jfc.gin.  8ft. oin. 


fe 

! 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

6 

II  II 

13  4 

14  9 

16  3 

17   2 

I7  8 

19   2 

20  7 

7 

13  6 

15   2 

1  6  lo 

18  7 

19  9 

20  3 

21  II 

23  9 

8 

15  i 

17  o 

19  o 

20  II 

22   3 

22  II 

24  10 

26  10 

9 

16  9 

18  IE 

21   I 

23  4 

24  10 

25  6 

27  9 

30  o 

10 

18  5 

20  10 

23  4 

25  9 

27  4 

28   2 

30  8 

33  2 

ii 

20   I 

22   9 

25  6 

28   2 

30  o 

30  ir 

33  8 

36  5 

12 

21  9 

24  8 

27  8 

30  8 

32  7 

33  7 

36  7 

39  7 

15 

26  10 

30  7 

34  3 

38  o 

40  6 

41  8 

45  5 

49  2 

To  use  these  tables  :  Having  first  measured 
the  distance  between  gauge  lines  of  the  two 
tracks,  refer  to  the  column  under  that  distance, 
and  opposite  the  frog  number  corresponding  to 
that  to  be  put  in,  will  be  found  the  diagonal 
distance  between  the  frog  points.  Measure  this 
carefully,  as  directed,  and  the  frog  point  will  be 
accurately  located.  Suppose  in  a  4  feet  8^  inch 
gauge  and  No.  9  frogs,  the  distance  between 
gauge  lines  or  tracks  is  7  feet,  what  is  the  diag- 
onal distance  ? 

By  reference  to  Table  No.  23,  under  7  feet  and 
opposite  No.  9  frog,  21  feet  6  inches  is  found  to 
be  the  distance  desired.  In  the  same  manner 
find  the  diagonal  distance  for  any  other  frogs. 


CR  OSS-  O  VERS  UPON  S  TRA IGHT  LINE.  8 1 

If  the  distance  between  gauge  lines  is  one  not 
given  in  the  tables,  then  find  the  frog  point  by 
the  rule  on  page  73,  or  take  the  difference  be- 
tween the  two  distances  nearest  that  which  the 
tracks  are  apart  and  divide  this  difference  by 
3,  and  add  one-third  or  two-thirds  of  it  to  the 
less  distance,  according  as  the  increase  is  i  or  2 
inches. 

Example:  What  is  the  diagonal  distance,  No. 
8  frogs,  4  feet  9  inch  gauge,  and  6  feet  1 1  inches 
between  gauge  lines  ? 

In  Table  No.  24,  17  feet  is  the  distance  for  6 
feet  9  inches  apart,  and  19  feet  for  7  feet  apart; 
the  difference  is  2  feet,  or  24  inches.  Twenty- 
four  divided  by  3,  equals  8  inches,  which  is 
equal  to  one-third  of  24;  two-thirds  of  24  are 
twice  8,  or  1 6  inches,  equal  to  i  foot  4  inches, 
which,  added  to  17  feet,  makes  18  feet  4  inches, 
or  the  diagonal  distance  for  6  feet  1 1  inches  be- 
tween tracks. 

Any  objection  to  setting  frogs  by  measure- 
ment, upon  the  ground  that  they  are  not  made  of 
the  correct  angle,  and,  therefore,  cannot  be  set 
accurately  in  that  way,  is  hardly  warranted  by 
the  facts,  as  generally  it  is  not  only  the  easiest 
way  but  the  best  one,  and  frogs  are  made  suffi- 
ciently accurate  to  enable  it  to  be  done  gen* 
erally. 


82  PRACTICAL  SWITCH  WORK. 

Although  it  is  well  to  bear  in  mind  that  the 
theoretical  frog  point  is\  the  one  from  or  to  which 
measurement  should  be  made,  there  is  no  objec- 
tion to  measuring  from  the  blunt  point  or  any 
other  well-defined  mark  at  the  frog  point,  pro- 
vided the  measurement  is  made  to  or  from  a 
corresponding  point  of  the  other  frog. 

Be  careful  to  set  the  second  frog  of  a  cross- 
over upon  a  long  tangent  exactly  right,  as  the 
good  alignment  of  a  long  tangent  is  easily  de- 
stroyed by  a  mistake  of  a  few  inches  in  locating 
the  second  frog. 

To  set  frogs  in  a  cross-over  practically,  a  good 
way  is  to  set  the  first  frog  and  lay  a  full  rail  at 
its  heel,  connecting  it  with  splices  to  the  frog; 
then  give  this  rail  for  its  entire  length  the  exact 
line  or  angle  of  the  frog  and  tack  it  with  spikes 
to  hold  it  in  line.  Place  the  track-gauge  per- 
pendicular to  this  rail  and  move  it  along  the 
rail  to  the  point  where  it  meets  the  gauge  line  of 
the  other  rail. 

This  point  will  be  the  location  of  the  point  of 
the  other  or  second  frog. 

Another  way  is :  Having,  as  before,  connected 
and  lined  a  rail  at  the  heel  of  the  frog  already 
in  track,  take  a  frog-board  corresponding  to  the 
frog  number  and  place  it  upon  the  frog  rail  of 
the  opposite  track,  keeping  its  side  exactly  par- 


CROSS-OVERS   UPON  STRAIGHT  LINE.  83 

allel  with  the  gauge  line,  and,  with  the  track- 
gauge  perpendicular  to  the  rail,  as  before,  move 
the  board  along  the  rail  to  the  point  where  the 
gauge  is  exact  at  both  the  point  and  the  heel 
of  the  frog-board,  and  the  frog  will  be  accurately 
located,  the  point  of  the  board  being  the  same 
as  the  point  of  the  frog. 


CROSS-OVERS  UPON  CURVES. 

On  account  of  the  wide  difference  in  the 
curvature  of  main-track  curves  it  is  impossible 
to  give  a  simple,  practical  rule  for  the  distance 
between  the  frogs  in  a  cross-over  upon  a  curve. 
When  one  is  to  be  put  in,  about  as  good  a 
method  as  any  is  to  set  the  frog  practically  by 
the  frog-board,  as  explained  OR  page  82,  in 


No.  12. 


which  case  the  alignment  between  the  frog 
points  may  be  straight  or  curved,  ac'.ording  to 
the  circumstances  or  the  desire.  If  the  curve  is 
sharp  and  a  No.  8  frog  or  less  is  used,  the  cur- 
vature of  the  lead  of  the  frog  upon  the  inside  of 
the  curve  will  be  very  sharp,  as  referred  to  at 
length  on  page  22.  This,  however,  could  be  re- 
duced by  making  a  curve  between  the  frog 
points  which  would  enable  a  frog  of  higher  num- 
ber than  otherwise  to  be  placed  upon  the  inside 
(84) 


CROSS-OVERS  UPON  CURVES.  85 

of  the  curve,  and  consequently  a  longer  lead  and 
less  curvature  could  be  obtained  for  it. 

The  amount  of  curvature  of  the  turnout  and 
also  that  desired  between  the  frog  points  will 
depend  upon  the  number  or  angle  of  the  frogs 
available  for  the  inside  of  the  curve. 

As  will  be  seen  by  Table  No.  25,  the  number 
of  the  frog  upon  the  inside  of  a  curve,  except  in 
frogs  less  than  No.  8,  is  always  less  than  that 
upon  the  outside  when  there  is  straight  line  be- 
tween them ;  and  also  the  frog  number  decreases 
as  the  curvature  and  distance  between  tracks 
increase. 

It  is  customary  to  place  in  a  cross-over  upon 
a  curve  two  frogs  of  the  same  number,  just  as  is 
done  upon  a  straight  line ;  but  frogs  only  as  high 
as  No.  7  will  give  straight  line  between  them 
when  the  tracks  are  6  to  8  feet  apart  and  the 
curvature  is  as  high  as  8  or  10  degrees. 

Two  No.  8  frogs  will  also  give  straight  line 
upon  curves  as  high  as  3  degrees  for  the  same 
distances  apart,  but  upon  curves  from  3  to  10 
degrees  they  will  give  straight  line  only  when 
distance  the  tracks  are  apart  is  less  than  7  feet 
3  inches. 

Whenever  two  frogs  of  the  same  number 
higher  than  No.  8  are  used,  it  is  necessary  to 
make  a  curve  between  them  and  to  find  the 


86  PRACTICAL  SWITCH  WORK. 

location  of  the  point  of  the  second  frog  practi- 
cally. But,  ordinarily,  straight  line  between  the 
frogs  is  sufficient,  and  it  can  be  obtained  if  the 
proper  combination  of  frogs  is  used. 

Table  No.  25  gives  the  combinations  of  the 
frogs  for  cross-overs  upon  curves,  and  also  the 
diagonal  distance  between  the  frog  points  A  to 
B,  as  shown  in  Diagram  12,  for  every  3  inches 
difference  in  distance  between  gauge  lines  of 
track  from  6  feet  6  inches  to  8  feet,  when  the 
line  between  the  frogs  is  straight,  the  first  frog 
located  being  upon  the  outside  of  the  curve. 

In  explanation :  Suppose  we  want  to  know 
the  number  of  the  second  frog  upon  the  inside 
of  a  curve,  and  also  where  its  point  will  be  if  a 
No.  10  is  placed  upon  the  outside  of  a  6-degree 
curve  and  the  distance  between  the  gauge  lines 
of  the  parallel  tracks  is  7  feet  5  inches.  Refer 
to  Table  No.  25,  under  7  feet  5  inches,  opposite 
No.  10,  the  outside  frog,  we  find  the  inside  frog 
is  a  No.  8,  and  the  diagonal  distance,  denoted 
by  "  D .  D.,"  from  the  other  frog  is  26  feet. 

In  Table  No.  6  we  find  that  the  curvature  of 
the  lead  of  the  No.  10  frog  so  placed  is  prac- 
tically a  straight  line,  and  in  Table  No.  5  that 
the  curvature  of  the  No.  8  is  15^-  degrees. 

Care  should,  therefore,  be  taken  not  to  have 
the  curvature  of  the  inside  frog  too  sharp. 


UPON  CURVES. 


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THREE-THROW   SWITCHES. 

Three-throw  switches  are  of  two  kinds,  viz.  : — 

1.  For  turning  to  opposite  sides. 

2,  For  turning  to  the  same  side. 


No.  13. 

In  both  cases  the  main  frogs  should  be  oppo- 
site each  other. 

The  middle  or  crotch  frog,  when  turning  to 
opposite  sides,  is  upon  the  centre  line  of  the 
main  track,  and  when  turning  to  the  same  side 


No.  14. 

if  is  upon  the  line  of  the  frog  rail  of  the  main 
track. 

On  account  of  not  having  frogs  of  suitable 
number,   it   has   sometimes   been    necessary  to 
place  one  of  the  main  frogs  back  of  the  other  in 
(89) 


9O  PRACTICAL  SWITCH  WORK. 

turning  to  the  same  side,  but  it  should  not  be 
done  if  it  can  be  avoided,  on  account  of  the 
short  and  insecure  guard  rail  which,  in  that  case, 
would  have  to  be  placed  opposite  the  rear  frog, 
and  also  because  it  cannot  be  made  a  finished 
piece  of  switch  work. 

The  lead  of  a  three-throw  in  both  cases, 
whether  the  switch  is  a  point  or  a  stub,  is  the 
same  as  that  of  a  corresponding  single  turnout, 
the  main-track  frog  determining  its  length  and 
curvature. 

In  a  three-throw  to  the  same  side,  the  throw 
will  be  the  distance  the  sliding  rail  moves  from 
the  first  track  to  the  second  ;  for  the  third  or  ex- 
treme inside  track  it  will  be  twice  what  it  is  for 
one  track.  Herein  is  one  of  the  principal  objec- 
tions to  a  three-throw  of  this  kind,  viz.,  the  too 
great  distance  the  slide  rail  has  to  move  to  con- 
form to  or  complete  the  curve  of  the  track 
farthest  away. 

In  regard  to  the  curvature  of  the  lead,  such  a 
combination  of  frogs  should  always  be  used  as 
will  give  a  nearly  regular  curve  from  the  head- 
block  to  the  frog  point ;  and  the  crotch  frog, 
where  the  curvature  is  sharp,  should  be  short  in 
length  from  toe  to  heel. 

The  number  of  the  crotch  frog  theoretically 
is  seven-tenths  the  number  of  the  main  frog,  but 


THREE-THROW  SWITCHES.  9! 

it  is  always  better  to  use  a  frog  of  the  nearest 
whole  number. 

In  a  point  three-throw  the  two  main  frogs 
should  be  opposite  each  other,  but  of  different 
numbers,  in  order  to  have  the  point  of  the 
switch  of  the  one  track  at  the  heel  or  back  of  the 
point  of  the  switch  of  the  other.  This  can  be 
accomplished  by  leads  of  different  lengths,  and 
it  applies  to  both  cases  of  three-throws,  to  the 
same  or  to  opposite  sides. 

In  a  stub  three-throw,  just  as  in  a  single  stub 
turnout,  the  practicable  length  of  the  switch 
rail  should  determine  what  is  the  highest  com- 
bination of  frogs  it  is  advisable  to  use,  as  there 
would  be  nothing  gained  by  using  frogs  which 
would  give  a  long  and  easy  curve  as  far  as  the 
head-block,  when  the  limited  length  of  the  switch 
rail  would  greatly  increase  it  beyond  that  point. 

As  27  feet  is  the  length  of  the  longest  practi- 
cable moving  rail,  a  No.  9  or  a  No.  10  three- 
throw  should  be  the  maximum  and  a  No.  6  the 
minimum  limit,  and  this  latter  only  for  turning 
to  opposite  sides. 

In  a  three-throw  to  the  same  side  the  main 
frogs  should  not  be  less  than  No.  8  nor  greater 
than  No.  10,  unless  it  is  upon  the  outside  of  a 
curve,  in  which  case  the  circumstances  should 
determine  the  combination  of  frogs. 


C)2  PRACTICAL  SWITCH  WORK. 

When,  however,  circumstances  would  warrant 
using  a  No.  12  three-throw,  the  comparative  in- 
creased curvature  of  the  switch  rail  should  not 
operate  against  doing  so,  if  the  object  is  to  ob- 
tain reduced  curvature  through  the  frogs. 

The  difficulty  experienced  in  putting  in  a 
three-throw  is  to  find  the  position  of  the  point 
of  the  crotch  frog. 

This  can  be  done  practically  in  this  manner: 
Having  first  set  both  main  frogs  and  given  good 
line  to  both  outside  rails,  or  as  they  will  be 
wh£n  the  three-throw  is  completed,  each  of  which 
should  be  the  gauge  of  the  track  distant  from 
the  crotch  frog,  find  with  a  tape-line  the  point 
between  the  gauge  lines  of  these  two  outer  rails 
just  lined,  where  the  distance  is  equal  to  twice 
the  gauge;  at  this  point  place  the  point  of  the 
crotch  frog. 

Or,  having  lined  the  outside  rails,  as  just  indi- 
cated, use  a  frog-board,  moving  it  to  the  point 
where  it  will  gauge  neatly  with  both  outside 
rails,  with  perhaps  slight  adjusting  of  their  line, 
and  at  this  point  place  the  point  of  the  crotch 
frog.  But  the  easiest  way  is  to  take  from  Tables 
Nos.  26  and  27  the  distance  between  the  main 
and  the  crotch  frog,  and,  measuring  along  the 
main  rail  from  A  to  B,  in  Diagrams  Nos.  13  and 
14,  place  the  frog  accordingly. 


THREE-THROW  SWITCHES. 


The  following  tables  give  the  necessary  dis- 
tances for  finding  the  position  of  the  crotch  frog 
by  measurement  :  — 

TABLE  No.  26. 
THREE-THROWS  TO  OPPOSITE  SIDES. 


4  FEET  8*^  INCH  GAUGE. 

4  FEET  9  INCH  GAUGE. 

Main  Frogs. 

Crotch  Frogs. 

Main  Frogs. 

Crotch  Frogs. 

No. 

Lead. 

No. 

Between 
Points. 

No. 

Lead. 

No. 

Between 
Points. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

6 

56       6 

4 

16      6 

6 

57      o 

4 

16      9 

7 

65      II 

5 

19        3 

7 

66      6 

5 

19      6 

8 

75      4 

6 

22        0 

8 

76      o 

6 

22        3 

9 

84      9 

6 

24,     9 

9 

85      6 

6 

25      o 

10 

94      2 

7 

27      6 

10 

95      o 

7 

27      9 

ii 

103      7 

8 

30      3 

ii 

104      6 

8 

30      6 

TABLE  No.  27. 
THREE-THROWS  TO  SAME  SIDE. 


4  FEET  Sl/z  INCH  GAUGE. 


4  FEET  9  INCH  GAUGE. 


Main  Frogs. 

Crotch  Frogs. 

Main  Frogs. 

Crotch  Frogs. 

No. 

Lead. 

No. 

Between 
Points. 

No. 

Lead. 

No. 

Between 
Points. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

6 

56        6 

4 

16      6 

6 

57      o 

4 

16      9 

7 

65      II 

5 

19        3 

7 

66      6 

5 

19      6 

8 

75      4 

6 

22         0 

8 

76       o 

6 

22        3 

9 

84      9 

6 

24      9 

9 

85      6 

6 

25      o 

10 

94      2 

7 

27       6 

10 

95      o 

7 

27      9 

ii 

103       7 

8 

30      3 

ii 

104      6 

8 

30      6 

94  PRACTICAL  SIV ITCH  WORK. 

In  a  three-throw  to  opposite  sides,  4  feet  S| 
inch  gauge  and  No.  8  frogs,  the  crotch  frog  cor- 
responding is  a  No.  6,  and  its  distance  from 
either  main  frog,  measured  along  the  main  rail 
to  opposite  its  point,  is  22  feet,  and  it  will  be  up- 
on the  centre  line  of  the  straight  or  main  track. 

For  4  feet  9  inch  gauge  and  No.  10  frogs  the 
corresponding  crotch  frog  is  a  No.  7,  and  its  dis- 
tance from  main  frogs  is  27  feet  9  inches.  The 
distance  between  frog  points  for  all  suitable 
frogs  is  found  in  the  columns  of  these  tables 
under  the  heading  "  Between  Points." 

First  locate  the  main  frog,  and  from  it  meas- 
ure the  distance  to  the  crotch  frog,  taken  from 
the  tables. 

In  a  three-throw  to  same  or  opposite  sides 
there  is  no  practical  difference  in  the  number  of 
crotch  frog  and  the  distance  between  the  frog 
points,  they  being  the  same  in  both  cases,  nor  is 
it  necessary  to  have  different  distances  between" 
points  for  4  feet  8J  inch  and  4  feet  9  inch 
gauges,  as  what  is  suitable  to  one  gauge  is  just 
as  suitable,  practically,  to  the  other,  and  the  same 
distance  can  be  used  for  either  gauge. 

The  theoretical  number  of  the  crotch  frog  is 
obtained  by  the  formula — 


THREE-THROW  SWITCHES.  g$ 

in  which  n  is  the  number  of  the  crotch  frog,  g 
the  gauge,  and  Rf  the  radius  of  the  curve  through 
the  crotch  frog. 

The  radius  Rf  of  the  curve  through  the  crotch 
frog  is  obtained  by  formula  — 


in   which   R  equals    the   radius   of    the   curve 
through  the  main  frog  and  g  the  gauge. 

The  theoretical  distance  between  the  main 
and  the  crotch  frog  is  obtained  in  this  way: 
First  find  the  distance  from  the  P.  C.  of  the 
turnout  to  the  point  of  the  crotch  frog,  which  is 
obtained  by  either  of  the  following  formulas: 
P.  C.  to  crotch  frog,  or  — 


equals,  approximately,   1.414  gn  ;   or  P.  C.   to 
crotch  frog,  or  — 


In  these  formulas  g  equals  the  gauge,  //  the 
number  of  main  frog,  c  the  number  of  crotch 
frog,  and  R  the  radius  of  the  curve,  /'  being 
equal  to  the  distance,  or  lead,  to  the  crotch  frog 
from  the  point  of  the  curve. 

Having  obtained  the  distance  from  the  point 
of  the  curve  to  the  crotch  frog,  subtract  it  from 


96  PRACTICAL  SWITCH  WORK. 

the  lead  of  the  main  frogs.  Suppose,  for  ex- 
ample, the  main  frogs  are  No.  10,  the  crotch 
frog  No.  7  and  the  gauge  4  feet  9  inches;  the 
lead  of  No.  i o  is  95  feet,  and  the  distance,  by 
the  formula,  to  the  crotch  frog  is  67  feet  3 
inches;  subtracting  this  from  the  lead,  we  have 
27  feet  9  inches  as  the  distance  between  the 
main  frog  and  the  crotch  frog. 

It  should  not  be  overlooked  that  the  crotch 
frogs  available  are  not  usually  of  an  angle  or 
number  exactly  corresponding  to  what  they 
should  be  according  to  theoretical  calculation. 

For  example:  In  a  No.  8  three-throw  the 
crotch  frog  is  No.  5T676o,  and  in  a  No.  9  it  is  6T3^. 
Such  fractional  numbers,  if  used  at  all,  are 
special  frogs,  No.  6  being  the  nearest  suitable 
standard  number,  and  should  be  used  with 
either  No.  8  or  No.  9. 

When  the  two  main  frogs  in  a  stub  three- 
throw  are  not  the  same  number,  generally  they 
should  not  be  placed  opposite  each  other,  but 
each  should  be  its  lead  distance  from  the  head- 
block. 

The  lead  of  a  three-throw  is  the  same  as  that 
of  a  single  turnout  having  the  same  number  of 
frog,  and  what  is  true  of  the  turnout  as  regards 
shortening  the  lead  is  also  true  of  the 
throw  whenever  it  may  be  desirable. 


THREE-  T*R  O  W  SWITCHES.  97 

Where  a  three-throw  switch  is  not  an  absolute 
necessity  it  should  not  be  put  in,  two  singles  al- 
ways being  preferable,  as  two  single  switches, 
into  which  nearly  every  three-throw  can  be  con- 
verted, are  safer  and  more  satisfactory. 


No. 

In  putting  in  a  three-throw,  first  determine  the 
position  of  the  main  frogs,  and  from  them,  by 
measurement,  locate  the  point  of  the  crotch  frog, 
which  can  easily  be  done  before  any  of  the  frogs 
are  set. 

Better  and  more  rapid  work  can  be  done  by 


No.  16 


using  the  tables  than  by  finding  the  position  of 
the  crotch  frog  practically,  provided  the  meas- 
uring is  done  accurately ;  at  the  same  time,  how- 
ever, there  should  be  no  objection  whatever  to 
locating  it  practically,  if  it  is  preferable  to  do  so, 
7 


98  PRACTICAL  SWITCH  WORK. 

As  has  already  been  mentioned,  it  sometimes 
happens  that  it  is  necessary  to  have  a  combina- 
tion of  single  turnouts,  which  is  equivalent  to  a 
three-throw,  as  sh'own  in  Diagrams  Nos.  15 
and  1 6. 

In  a  case  of  this  kind  it  is  better  to  place  the 
main  frogs  opposite  each  other.  There  should 
be  such  a  difference  in  their  number,  and  conse- 
quently such  a  difference  in  their  leads,  that  the 
point  of  the  switch  or  the  head-block  of  the 
shorter  lead  could  be  placed  at  or  near  the  heel 
of  the  switch  point  of  the  longer  lead,  the  ob- 
ject being  to  obtain  what  is  equivalent  to  a  three- 
throw  and  yet  not  having  the  same  head-block. 

In  a  stub  switch  there  is  no  necessity  of  hav- 
ing frogs  of  different  numbers,  as  in  that  case 
there  would  be  the  same  head-block  and  each 
frog  would  be  the  lead  distance  from  the  head- 
block,  and,  therefore,  opposite  each  other. 

Suitable  combinations  of  frogs  and  distances 
between  points  for  cases,  shown  in  Diagrams  Nos. 
15  and  1 6,  are  given  in  the  following  tables : — 


THREE-THROW  SWITCHES. 


99 


^  TABLE  No.  28. 

FOR  4  FEET  8}4  INCH  AND  4   FEET  9   INCH    GAUGES. 

Three-throws  to  opposite  sides. 


FROGS. 

DISTANCE 
FROG 

BETWEEN 
POINTS. 

FROM 
CENTRE  LINE. 

Main. 

Crotch. 

No. 
10  and  8 

No. 
6 

Feet. 
23 

Inches. 
6 

Inches. 

*X 

1  1  and  9 

7 

27 

3 

*>A 

To  same  side. 


io  and  8 
1  1  and  9 

6 
7 

24 

27 

8 

6       ' 

./• 

In  the  case  of  a  three-throw  to  opposite  sides 
for  these  combinations  of  frogs,  the  point  of  the 
crotch  frog  will  not  be  upon  the  centre  line  be- 
tween the  rails  of  the  main  track,  but  will  be 
about  2j  inches  from  the  centre  line,  and  always 
upon  that  side  nearer  the  main  frog  of  the  higher 
number. 

For  example :  It  will  be  upon  the  side  nearer 
the  No.  ii  frog  in  a  combination  of  Nos.  11,9, 
and  7,  and  upon  the  side  nearer  the  No.  10  in  a 
10,  8,  and  6  combination. 

When  the  main  frogs  are  of  the  same  number 
and  opposite  each  other,  the  point  of  the  crotch 
frog  is  always  exactly  half  way  between  the 
rails,  or  upon  the  centre  line  of  the  track. 


A  "LADDER"  TRACK. 

The  arrangement  of  turnouts  at  the  end  of  a 
yard,  as  shown  below,  is  called  a  "ladder." 

It  is  the  most  simple  and  practicable  method 
of  connecting  yard  tracks,  the  point  of  all  the 
frogs  being  at  the  intersection  A  of  the  frog  rail 
of  the  parallel  yard  tracks  with  the  frog  rail  of 
the  ladder  track,  forming  a  series  of  single  turn- 
outs from  a  straight  line. 


No.  17. 


All  the  yard  tracks  need  not  be  the  same 
distance  apart,  although  it  is  better  that  they 
should  be  so  ;  but  they  must  be  parallel. 

All  the  frogs  must  be  of  the  same  number, 
and  the  direction  of  the  ladder  track  must  ex- 
actly correspond  to  the  angle  of  the  first  frog 
in  it. 

The  principal  difficulties  to  be  encountered  in 
the  work  of  putting  in  a  ladder  are  :  First,  to 

(100) 


A  "LADDER"    TRACK.  IOI 

obtain  its  correct  direction ;  that  is,  to  mark  or 
stake  out  upon  the  ground  the  line  of  the  angle 
of  the  frogs  to  be  used ;  and,  Second,  to  find  the 
location  of  the  points  of  all  the  frogs  on  that  line. 

When  it  can  be  done,  where  three  or  four 
tracks  are  to  be  so  connected,  it  is  better  to  have 
the  services  of  an  engineer  with  an  instrument 
to  give  the  direction  of  the  ladder,  but  if  that  is 
impossible,  by  following  the  directions  on  page 
102,  any  trackman  can  do  it  well  enough  him- 
self. The  mistake  which  is  usually  made  by 
trackmen  is,  that  having  put  in  the  first  turn- 
out or  switch  of  the  ladder,  they  continue  with 
the  others,  lining  them  in  with  the  first  one,  and, 
by  the  time  three  or  four  have  been  put  in,  the 
ladder  is  invariably  found  to  be  out  of  line,  and 
it  becomes  more  so  as  the  number  of  frogs  in  it 
increases. 

The  location  of  the  points  of  the  frogs  in  a 
ladder  can  be  ascertained  theoretically  by  calcu- 
lating the  distance  between  them,  and,  begin- 
ning with  the  first  frog,  measuring  the  distance 
along  the  frog  rail  of  the  ladder,  and  locating 
each  frog  in  order  by  measurement.  That  is  the 
easiest  and  best  way  to  do  it.  It  can  also  be 
obtained  practically  as  explained  on  page  109. 
Either  way,  if  done  accurately,  will  be  satis- 
factory. 


IO2  PRACTICAL  SWITCH  WORK. 

The  distance  between  the  frog  points  in  a 
ladder  will  vary  according  to  the  distance  the 
parallel  tracks  are  apart ;  and,  as  it  simplifies  the 
work,  so  far  as  possible  all  the  tracks  should  be 
a  uniform  distance  apart. 

The  Tables,  Nos.  30  and  31,  give  the  calculat- 
ed distance  between  the  points  of  the  frogs  in  a 
ladder  for  distances  between  the  gauge  lines  of 
the  parallel  tracks  from  6  feet  6  inches  to  8  feet, 
and  can  be  used  in  locating  the  frogs  by  measure- 
ment. The  diagram  below  shows  how  to  obtain 
the  direction  of  a  ladder  track. 


No.  18. 

To  mark  upon  the  ground  the  direction  of  the 
frog  rail  of  a  ladder,  as  from  A  to  C,  first  decide 
upon  the  location  of  the  point  of  the  first  frog,  as 
at  A.  This  frog  we  will  suppose  to  be  a  No.  8; 
all  the  frogs  in  the  ladder  should,  therefore,  be 
No.  8. 

By  referring  to  Table  No.  29,  we  find  that  for 
a  No.  8  frog  the  distance  from  the  straight  or 
main  track  to  the  gauge  line  of  the  frog  rail  of 
the  ladder  opposite  a  point  B,  300  feet  from  the 


A  "LADDER"    TRACK.  JO3 

point  of  the  first  frog  at  A,  is  37  feet  7J  inches, 
as  shown  in  the  diagram. 

Measure  300  feet  from  the  point  of  the  frog, 
and  exactly  at  a  right  angle  from  the  gauge  line 
of  the  rail  at  B  measure  37  feet  7f  inches  to  C. 
C  will  be  a  point  on  the  gauge  line  of  the  frog 
rail  of  a  No.  8  ladder.  Two  points  on  the  line 
of  the  ladder  will  thus  be  established,  one  at  A 
and  the  other  at  C. 

Drive  a  stake  at  C  and  place  a  tack  in  it  ex- 
actly 37  feet  7f  inches  from  the  gauge  of  the 
rail  at  B,  and  stretch  a  string  from  the  point  of 
frog  at  A  and  fasten  it  to  the  tack  in  the  stake 
at  C.  If  done  accurately,  the  direction  of  the 
string  will  be  the  direction  of  the  No.  8  ladder, 
and  the  angle  that  of  a  No.  8  frog. 

Any  other  of  the  distances  in  the  table,  meas- 
ured from  the  points  at  100  to  500  feet  from  the 
point  of  the  first  frog,  will  give  the  same  direc- 
tion as  that  measured  at  the  3OO-foot  point.  If 
all  the  measurements  in  the  table  were  made  in 
the  same  manner  as  that  from  B  to  C,  the  stakes 
at  each  point  would  be  in  the  same  straight  line. 

If  the  ladder  is  to  connect  with  a  number  of 
yard  tracks  the  measurement  should  be  taken 
from  the  farthest  or  5OO-foot  point,  because  the 
line  giving  the  direction  of  the  ladder  should  be 
as  long  as  possible. 


IO4  PRACTICAL  SWITCH  WORK. 

To  insure  accuracy,  it  should  be  observed,  be- 
fore any  offset  measurements  are  made,  that  the 
straight  track  in  which  the  first  frog  is  placed  is 
in  good  alignment  with  the  remainder  of  the 
tangent  beyond  the  point  opposite  where  the  end 
of  the  ladder  will  be. 

A  carpenter's  iron  square,  or  a  large  wooden 
square,  should  be  used  to  obtain  the  right  angle 
in  measuring  from  the  straight  track,  as  at  B,  to 
the  ladder  line  at  C. 

A  good  metallic  tape-line,  a  new  one  preferred, 
should  be  used  and  the  measurements  made 
very  accurately. 

To  further  insure  accuracy,  it  is  well  to  take 
measurements  from  two  points  and  test  them 
until  they  agree  and  are  in  the  same  ladder  line. 

The  offset  measurements  could  be  made  for  a 
No.  8  ladder  from  the  200  and  4OO-foot  points, 
and  would  be  25  feet  \\  inches  and  50  feet  2f 
inches,  respectively,  taken  from  Table  No.  29. 


A   "LADDER"    TRACK. 

TABLE  No.  29. 


105 


SHOWING  DISTANCES  BY  WHICH  THE  DIRECTION  OF 
THE  FROG  RAIL  OF  LADDER  CAN  BE  OBTAINED  AND 
LAID  OUT  UPON  THE  GROUND  FOR  FROGS  FROM 
No.  6  TO  NO.  12  FOR  ANY  GAUGE. 


DISTANCE   FROM   STRAIGHT  TRACK  TO  GAUGE  LINE  OF 

FROG  RAIL  OF  LADDER  AT 

FROG 

No. 

100  Feet. 

200  Feet. 

300  Feet. 

400  Feet. 

500  Feet. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

Ft.      In. 

Ft.    In. 

6 

16    9^ 

33    6^ 

50    4X 

67      iji 

83   II 

7 

14    4# 

28    8^3 

43     i 

57     5X 

71     9# 

8 

12      6^§ 

25      I# 

37   yM' 

5O      2^ 

62     9 

9 

ii     i^ 

22      2)1A 

33    5^ 

44    6J^ 

55    8>6 

10 

10      O^j 

20      0^ 

30    i 

40   i>< 

50     i^ 

II 

9     1^4 

18    2^ 

27     4 

36  &{ 

45    6>^ 

12 

8    4/s 

16    8^ 

25    o,1^ 

33    4.^ 

41     S^j 

To  FIND  THE  LOCATION  OF  THE  FROG  POINTS 
IN  A  LADDER  TRACK. 

After  having  established  the  direction  of  the 
ladder  track,  the  next  thing  is  to  find  the  po- 
sition of  the  frogs  in  it.  This  will  depend  upon 
the  number  or  angle  of  the  frog  and  the  distance 
the  parallel  tracks  are  apart. 

The  best  way  to  do  is  to  locate  the  frogs  by 
measurement,  calculating  the  distance  between 
the  points,  and  then,  beginning  with  the  first 
frog,  as  at  A,  if  all  the  frogs  are  the  same  dis- 
tance apart  (which  they  should  be),  the  distance 


IO6  PRACTICAL  SWITCH  WORK. 

between  the  points  can  be  measured  and  the 
position  of  each  frog  known  exactly. 

This  calculated  distance  is  obtained  by  using 
the  formula :  c  =  -^—-^  which  means  that  the 
distance  A  to  B  in  the  diagram,  or  from  the 
point  of  one  frog  to  the  point  of  the  other,  is 
equal  to  the  distance  between  the  parallel  tracks 
divided  by  the  Sine  of  the  frog  angle. 

The  distances  in  the  following  tables  for  4 
feet  8J  inch  and  4  feet  9  inch  gauges,  and  for 
distances  between  gauge  lines  of  parallel  tracks 


No.  19. 

from  6  feet  6  inches  to  8  feet,  are  calculated  by 
this  formula. 

Suppose  it  is  desired  to  know  the  distance  be- 
tween frog  points  in  a  No.  9  ladder,  gauge  4  feet 
8%  inches,  and  tracks  7  feet  between  gauge  lines. 

In  Table  No.  30,  opposite  No.  9  frog,  and  un- 
der 7  feet  o  inches,  105  feet  8£  inches  is  found 
to  be  the  distance  desired. 

Also,  what  is  the  distance  between  frog  points 
in  a  No.  8  ladder,  gauge  4  feet  9  inches,  and 
tracks  7  feet  5  inches  apart  ?  See  page  109. 


A  "LADDER"    TRACK. 


107 


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A   "LADDER"    TRACK. 

In  Table  No.  31,  opposite  No.  8  frog,  and 
under  7  feet  5  inches,  it  is  found  to  be  97  feet 
8|  inches. 

In  using  the  distances  in  these  tables,  measure- 
ments should  always  be  taken  between  the  the- 
oretical frog  points,  not  the  blunt  points,  unless 
allowance  has  been  made  in  measuring  from  the 
first  frog,  in  which  event  measurements  may  be 
made  between  the  blunt  points. 

The  frog  points  can  also  be  found  practically, 
but  not  so  easily,  by  using  a  string  and  finding 
the  intersection  of  the  parallel  tracks  with  the 
line  of  the  ladder  track  in  this  way : — 

To  whatever  distance  the  tracks  are  apart  add 
the  gauge  of  the  track.  For  example:  If  they 
are  7  feet  3  inches  and  the  gauge  is  4  feet  9 
inches,  the  table  distance  between  gauge  lines 
would  be  12  feet.  Drive  a  stake  upon  each  side 
of  the  ladder  track,  and  place  a  tack  in  it  12  feet 
from  the  gauge  of  the  main-track  rail  and  stretch 
a  string  between  them. 

The  string  will  correspond  to  the  gauge  line 
of  the  parallel  track,  and  its  intersection  with  the 
string  giving  the  direction  of  the  ladder  will  be 
the  frog  point. 

For  the  second  parallel  track  the  distance  will 
be  twice  12,  or  24  feet,  and  for  the  third,  36  feet, 
and  so  on,  adding  1 2  feet  for  each  additional  track. 


I  IO  PRACTICAL  SWITCH  WORK. 

If  done  accurately,  the  points  so  obtained  will 
be  the  same  as  those  obtained  from  the  tables. 

A  ladder  composed  of  No.  8,  9,  or  10  frogs  is 
the  most  practicable. 

A  three-throw  ladder  is  not  impracticable,  but 
it  is  not  advisable,  as  a  single  ladder  is  much 
superior. 


SWITCH  TIMBER. 

It  is  too  much  to  give  here  a  bill  of  timber  for 
every  variation  possible  in  a  turnout  or  cross- 
over. The  bills  which  are  given  are  for  frogs 
from  Nos.  6  to  15,  for  the  theoretical  lead,  for  4 
feet  8J  inch  or  4  feet  9  inch  gauges,  and  distance 
between  centres  of  switch  timber  22  inches. 
They  are  suitable  to  cross-ties  8  feet  6  inches 
long,  and,  in  the  case  of  cross-overs,  are  for  dis- 
tances between  gauge  lines  of  parallel  tracks 
from  6  feet  6  inches  to  8  feet. 

These  bills  can  easily  be  changed  to  suit  any 
variation  from  these  conditions  as  a  basis.  For 
example:  For  a  short  lead,  by  omitting  a  certain 
number  of  the  pieces  near  the  switch  point. 

The  number  of  pieces  in  any  bill  depends  upon 
the  distance  apart  it  is  necessary  to  have  them 
and  also  upon  the  lead. 

Generally,  for  large  hewn  timber  the  distance 
between  centres  should  be  about  24  inches ;  for 
timber  sawed  upon  the  four  sides,  and  having  10 
inches  face,  it  should  be  about  22  inches ;  and 
for  small  timber,  having  8  inches  face,  it  should 
be  about  20  inches.  About  the  best  size  for 
switch  timber  is  7  inches  thick,  10  inches  face, 
(i  ix) 


112  PRACTICAL  SWITCH  WORK. 

and  distance  between  centres  of  pieces  22  inches, 
or  about  12  inches  apart.  The  thickness  should 
be  the  same  as  that  of  cross-ties,  and  should  not 
be  less  than  6£  nor  more  than  7  inches. 

Knowing  the  distance  between  centres,  the 
number  of  pieces  between  the  switch  and  the 
frog  point  can  be  determined  by  reducing  the 
lead  to  inches  and  dividing  it  by  the  distance 
between  centres.  For  example  :  A  lead  of  76 
feet  for  a  No.  8  frog  is  equal  to  912  inches; 
dividing  912  by  22  inches,  the  distance  between 
centres,  41  pieces  are  found  to  be  required  be- 
tween the  head-block  and  the  frog  point.  It  is 
impossible  to  space  the  timber  the  exact  dis- 
tance apart  on  account  of  the  rail  joints,  but  the 
number  of  pieces  obtained  in  this  manner,  disre- 
garding the  joints,  is  sufficient  for  a  good  bill. 

The  length  for  each  piece  is  more  difficult  to 
obtain,  if  it  is  desired  to  make  the  bill  conform 
to  the  line  of  the  turnout  curve.  One  way 
which  will  give  regularly  increasing  lengths,  not 
conforming  to  the  curve,  however,  is  to  reduce 
to  inches  the  difference  between  the  lengths  of 
the  cross-tie  at  the  head-block  and  the  switch-tie 
under  the  frog  point,  and  divide  this  difference 
by  the  number  of  pieces  necessary  between  the 
head-block  and  the  frog  point.  The  length  so 
obtained  should  be  added  to  each  piece,  begin* 


SWITCH   TIMBER.  IIj 

ning  with  the  8  or  8^  foot  cross-tie  at  the  head- 
block,  and  thus  increase  to  the  proper  length  un- 
der the  frog  point  and  also  to  the  last  long  piece. 

If,  for  example,  the  piece  under  the  frog  is  13 
feet  3  inches  and  the  cross-ties  are  8  feet  6  inches 
long,  the  difference  between  them  is  4  feet  9 
inches,  or  57  inches.  Fifty-seven  inches  divided 
by  41,  the  number  of  pieces  between  the  head- 
block  and  the  frog,  give  about  i^  inches  differ- 
ence, which  should  be  added  to  each  piece  so  as 
to  increase  in  41  pieces  from  8  feet  6  inches  to 
13  feet  3  inches. 

When  all  the  pieces  are  in  position  the  pro- 
jecting ends  can  be  chopped  off  so  as  to  conform 
to  the  turnout  curve,  if  it  is  so  desired. 

But  to  make  a  bill  conform  to  the  turnout 
curve,  the  formula,  or  way  of  calculating  the 
stiib  lead,  on  page  30,  can  be  used,  as  by  it  the 
position  of  certain  pieces  can  be  calculated,  and 
having  it  and  also  their  length,  the  remaining 
pieces  can  be  easily  placed  between  them.  If,  by 
assuming  that  every  6  inches  difference  in  the 
length  of  the  pieces  is  equal  to  the  throw  of  a 
stub  switch,  the  piece  which  belongs  at  each 
throw  will  be  a  distance  from  the  frog  point 
equal  to  the  stub  lead  for  the  same  throw ;  that 
is,  if  the  first  throw  is  6  inches,  the  second  12 
inches,  the  third  18  inches,  and  so  on,  until  the 
8 


114 


PRACTICAL  SWITCH  WORK. 


throw  nearly  equals  the  gauge,  the  position  of 
each  piece  can  be  determined,  and,  by  adding 
the  intervening  pieces,  the  bill  can  be  completed. 
For  cross-ties  8^  feet  long,  the  following  table 
gives  the  throw  and  length  of  the  correspond- 
ing piece  :  — 

Where  the  throw  is  6    inches,  the  piece  is  9     feet  long. 
i    foot 

1  X  feet 

2  " 


3 

3X 

4 


YO 

10)4 

II 

n)4 

12 
12)4 


If  the  cross-ties  are  8  instead  of  8-J  feet  L',ng 
the  pieces  will  be  6  inches  less.  At  the  7ro^ 
point  the  length  of  the  piece  is  equal  to  the  4 
feet  9  inch  gauge  added  to  the  length  of  the? 
cross  tie,  8  £  feet,  making  13  feet  3  inches,  and 
a  cross-tie  8  feet  long  added  to  4  feet  9  inches  i;, 
12  feet  9  inches.  This  method  should  be  used 
only  as  a  help  in  making  a  bill  which  curves 
with  the  turnout. 

It  is  hardly  worth  while  to  spend  much  time 
making  out  with  exactness  a  bill  of  timber,  as  it 
is  rarely,  if  ever,  cut  according  to  the  bill,  and  to 
have  a  finished  piece  of  work  it  is  invariably  nec- 
essary to  chop  off  the  ends  to  a  certain  length. 

The  governing  pieces  are  the  head-block,  geu* 


SWITCH   TIMBER.  IlJ 

erally  about  12  feet  long,  the  frog-tie,  that  is, 
the  piece  under  the  frog  point,  13  feet  3  inches 
long  for  cross-ties  8  feet  6  inches,  and  12  feet  9 
inches  long  for  cross-ties  8  feet  long,  and  the 
last  long  piece  back  of  the  frog,  which  is  about 
1 6  feet  or  16  feet  6  inches  long. 

If  these  governing  pieces  are  first  placed  in 
their  proper  position,  all  the  other  intervening 
ones  will  naturally  fall  into  their  places  when 
putting  in  the  timber. 

By  deducting  6  inches  from  each  piece,  these 
bills  for  8|-  feet  cross-ties  can  be  changed  to  suit 
cross-ties  8  feet  long. 

The  number  of  pieces  back  of  the  frog  is  op- 
tional, about  1 6  feet  being  a  good  length  for  the 
last  long  piece. 

Divide  the  distance,  in  inches,  between  the 
frog  point  and  last  long  tie  by  the  distance  be- 
tween centres,  to  ascertain  the  number  of  pieces 
back  of  the  frog  point. 

The  following  bills  are  for  the  theoretical 
lead,  8f  feet  cross-ties  and  about  22  inches  be- 
tween centres. 

If  a  shorter  lead  is  used,  it  is  necessary  to 
omit  some  of  the  pieces,  not  back  of  the  frog, 
but  beyond  the  heel  of  the  switch,  where,  on 
account  of  the  length  of  the  theoretical  lead,  the 
turnout  curve  is  flat. 


n6 


PRACTICAL  SWITCH  WORK. 


No  complete  bills  are  given  for  cross-Overs, 
yet  «nough  is  given  in  Tables  Nos.  32  and  33  to 
enable  a  bill  to  be  easily  made.  First  ascertain 
from  the  tables,  according  to  the  distance  the 
tracks  are  apart,  how  many  long  pieces  are  re- 
quired, and  also  the  length  of  the  last  short 
piece.  The  single  bill  for  the  corresponding 
frog  up  to  the  last  short  piece  can  be  used  to 
complete  the  cross-over  bill. 

BILL  FOR  No.  6,  SINGLE. 

Gauges,  4  feet  8}4  inches  and  4  feet  9  inches. 
Theoretical  lead,  57  feet. 
Between  centres,  22  inches. 
Cross-tie,  S*4  feet. 


PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In- 

12   0 

9  u 

10  O 

ii  3 

J2   9 

14  4 

4 

8  6 

9   2 

10   2 

ii  6 

13   0 

14  8 

8  7 

9  4 

u  4 

ii  9 

13  3 

15  0 

8  8 

9  6 

10  6 

12   0 

13  6 

15  4 

8  9 

9  8 

10  9 

12  3 

13  9 

•5  8 

8  10 

9  10 

II   0 

12   6 

14  o 

16  o 

For  stub  lead,  omit  the  first  eight  or  ten 
pieces  under  the  switch. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the  last  two  pieces. 

The  piece  which  belongs  under  the  frog  point 
is  13  feet  3  inches  for  8J  feet  cross-tie,  and  12 
feet  9  inches  for  8  feet  cross-tie. 


SWITCH    TIMBER. 

FOR  No.  7,  SINGLE. 

Gauges,  4  feet  8)4  inches  and  4  feet  9  inches. 
Theoretical  lead,  66  feet  6  inches. 
Between  centres,  22  inches. 
Cross-tie,  8}4  feet. 


117 


PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

12   O 

9   \ 

10   2 

II  6 

13  6 

15  6 

4 

8  6 

9  2 

10  4 

II  9 

13  9 

*5  9 

8  7 

9  3 

10  6 

12  O 

14  0 

16  o 

8  8 

9  4 

10  8 

12  3 

U  3 

16  3 

8  9 

9  6 

10  10 

12.  6 

14  6 

16  6 

8  10 

9  8 

II   0 

12  9 

14  9 

8  ii 

9  Jo 

11   2 

13  o 

15  o 

9  o 

10   O 

ii  4 

'3  3 

i5  3 

For  stub  lead,  omit  the  first  eight  or  ten  pieces. 
For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the  last  four  pieces. 

FOR  No.  8,  SINGLE. 

Gauges,  4  feet  8%  inches  and  4  feet  9  inches. 
Theoretical  lead,  76  feet. 
Between  centres,  22  inches. 
Cross-tie,  8%  feet. 


PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

12  0 

9  o 

9  7 

10  6 

ii  9 

13  3 

15  0 

6 

8  6 

9  i 

9  8 

10  8 

12  O 

13  6 

15  3 

8  7 

9  2 

9  ID 

10  10 

12  3 

13  9 

15  6 

8  8 

9  3 

10   O 

II   0 

12   6 

14  o 

15  9 

8  9 

9  4 

10   I 

II   2 

12  9 

14  3 

16  o 

8  10 

9  5 

10   2 

ii  4 

13  o 

14  6 

16  3 

8  ii 

9  6 

10  4 

ii  6 

13  I 

14  9 

16  6 

PRACTICAL  SWITCH  WORK. 


For  72  feet  short  lead,  omit  the  two  pieces 
near  the  switch,  but  not  under  it. 

For  stub  lead,  omit  the  first  eight  or  ten  pieces. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the  last  five  pieces. 

FOR  No.  9,  SINGLE. 

Gauges,  4  feet  8X  and  4  feet  9  inches. 
Theoretical  lead,  85  feet  6  inches. 
Between  centres,  22  inches. 
Cross-tie,  8>^  feet. 


PCS. 

Ft.  In. 

PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

12   O 

2 

9  2 

10   2 

ii  6 

13  o 

15  3 

6 

8  6 

2 

9  3 

10  4 

ii  8 

13   3 

15  6 

8  7 

9  4 

10  6 

II  10 

13   6 

15  8 

8  8 

9  5 

10  7 

12   0 

J3  9 

15  10 

8  9 

9  6 

10  8 

12   2 

14  o 

16  o 

8  10 

9  7 

IO  IO 

12  4 

14  3 

16  3 

8  ii 

9  8 

II   O 

12   6 

14  6 

16  6 

2 

9  o 

9  10 

II   2 

12   8 

14  9 

2 

9  i 

IO   0 

ii  4 

12  IO 

15  o 

For  76  feet  6  inches  short  lead,  omit  four  of 
the  duplicate  pieces  longer  than  9  feet. 

For  stub  lead,  omit  first  twelve  or  fourteen 
pieces. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the  last  five  pieces. 


FOR  No.  10,  SINGLE. 

Gauges,  4  feet  8)4  and  4  feet  9  inches. 
Theoretical  lead,  95  feet. 
Between  centres,  22  inches. 
Cross-tie,  8>£  feet. 


PCS. 

Ft.  In. 

PCS. 

Ft.  In, 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

12  0 

2 

9  3 

10   I 

II   4 

13  o 

15  2 

5 

8  6 

2 

9  4 

10   2 

II   6 

13   I 

15  4 

8  7 

9  5 

10  3 

ii  8 

13  3 

15  6 

8  8 

9  -6 

10  4 

II  10 

13  6 

15  8 

8  9 

9  7 

10  6 

12   O 

13  9 

15  10 

8  10 

9  3 

10  8 

12   2 

14  o 

16  o 

8  ii 

9  9 

10  IO 

12  4 

14  3 

16  2 

9  o 

9  10 

II   O 

12   6 

14  6 

16  4 

2 

9  I 

9  ii 

n*  i 

12   8 

14  9 

16  6 

2 

9  2 

10   O 

II   2 

12  10 

15  o 

For  85  feet  short  lead,  omit  the  five  duplicate 
pieces  longer  than  9  feet. 

For  stub  lead,  omit  the  first  sixteen  or  seven- 
teen pieces. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  last  six  pieces. 


120 


PRACTICAL  SWITCH. 


FOR  No.  ii,  SINGLE. 

Gauges,  4  feet  8)4  and  4  feet  9  inches. 
Lead,  104  feet  6  inches. 
Between  centres,  22  inches. 
Cross-tie,  S)4  feet. 


PCS. 

Ft.  In. 

PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  Jnv 

12   O 

2 

9  4 

IO  4 

II  8 

13  6 

15  4 

6 

8  6 

2 

9  5 

10  6 

II  IO 

13  8 

15  6 

8  7 

2 

9  6 

10  7 

12   0 

13  10 

15  8 

8  8 

9  7 

10  8 

12   2 

14  o 

15  10 

8  9 

9  8 

10  10 

12  4 

14   2 

16  o 

8  10 

9  9 

II   O 

12   6 

14  4 

16  2 

8  ii 

9  10 

ii  I 

12   8 

14  6 

16  4 

2 

9  o 

9  ii 

II   2 

12  IO 

14  8 

16  6 

2 

9  I 

IO   0 

ii  4 

13   0 

14  10 

2 

9  2 

IO   2 

ii  6 

13   I 

15   0 

2 

9  3 

10  3 

ii  7 

13  3 

15   2 

For  88  feet  short  lead,  omit  the  seven  dupli- 
cate pieces. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the  last  six  pieces. 


SW2TCJJ  T 


121 


FOR  No.  12,  SINGLE. 

Gauges,  4  feet  8}4  and  4  feet  9  inches. 
Lead,  114  feet. 
Between  centres,  22  inches. 
Cross-tie,  S)4  feet. 


PCS. 

Ft.  In. 

PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

I  12   0 

2 

9  4 

10  4 

II   8 

13  4 

15   2 

6 

8  6 

2 

9  5 

10  6 

II  IO 

13  6 

15   4 

8  7 

2 

9  6 

10  7 

12   O 

13  8 

15  6 

8  8 

2 

9  7 

10  8 

12   2 

13  10 

15  8 

8  9 

2 

9  8 

10  9 

12  4 

14  o 

15  10 

8  10 

9  9 

10  10 

12   6 

14   2 

16  o 

8  ii 

9  10 

II   O 

12   8 

14  4 

16  2 

2 

9  o 

9  ii 

ii  i 

12  IO 

14  6 

16  4 

2 

9  i 

IO   O 

II   2 

13   0 

14  8 

16  6 

2 

9  2 

IO   2 

ii  4 

13   I 

14  10 

2 

9  3 

10  3 

ii  6 

13  3 

15  o 

For  96  feet  short  lead,  omit  the  nine  duplicate 
pieces  longer  than  9  feet. 

For  stub  lead,  omit  the  first  twenty  pieces,  in- 
cluding duplicates,  except  those  under  switch. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  the.  last  six  pieces. 


122 


PRACTICAL  SWJTCH 


FOR  No.  15,  SINGLE. 

Gauges,  4  feet  8}4  inches  and  4  feet  9  inches. 
Lead,  142  feet  6  inches. 
Between  centres,  22  inches. 
Cross-tie,  8^  feet. 


PCS. 

Ft.  In. 

PCS. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

Ft.  In. 

12  O 

2 

9  7 

10  9 

II  II 

13  2 

14  4 

6 

8  6 

2 

9  8 

10  10 

12   0 

13  3 

14  6 

8  7 

9  9 

IO  II 

12   I 

13  4 

14  8 

8  8 

9  10 

II   O 

12   2 

13  5 

14  10 

8  9 

9  " 

IT  i 

12  3 

13  6 

15  0 

8  10 

IO   O 

II   2 

12  4 

13  7 

15  2 

8  ii 

10   I 

ii  3 

12   6 

13  8 

15  4 

2 

9  o 

10   2 

ii  4 

12  7 

13  9 

15  6 

2 

9  i 

10  3 

ii  5 

12   8 

13  10 

15  8 

2 

9  2 

10  4 

ii  6 

12  9 

13  ii 

>5  10 

2 

9  3 

10  5 

ii  7 

12  10 

14  o 

16  o 

2 

9  4 

10  6 

ii  8 

12  II 

14  i 

16  2 

2 

9  5 

10  7 

ii  9 

13  o 

14   2 

16  4 

2 

9  6 

10  8 

II  10 

13   I 

14  3 

16  6 

For  1 20  feet  short  lead,  omit  nine  duplicate 
pieces  longer  than  9  feet. 

For  8  feet  cross-tie,  use  pieces  6  inches  shorter 
and  omit  last  six  pieces. 

To  make  a  bill  for  No.  8  cross-over,  if  the 
distance  between  the  gauge  lines  is  7  feet  6 
inches,  and  to  suit  8  feet  6  inch  cross-tie,  look 
in  Table  No.  32,  and  under  7  feet  6  inches,  12 
feet  3  inches  is  found  to  be  the  length  of  the 
last  short  piece  and  20  feet  9  inches  the  length 
of  the  long  pieces.  In  Table  No.  33,  for  No.  8 


SWITCH    TIMBER.  12$ 

cross-over,  under  7  feet  6  inches,  we  find  that  21 
long  pieces  are  necessary. 

As  12  feet  3  inches  is  the  length  of  the  last 
short  piece,  all  the  pieces  preceding  it  in  the 
bill  for  No.  8  single,  on  page  117,  are  necessary 
to  complete  this  bill  for  one  end  of  the  cross- 
over. Add  these  same  pieces  for  the  other  end, 
observing  to  omit  certain  pieces,  as  directed,  if 
a  short  lead  is  used.  The  number  of  pieces  for 
this  No.  8  cross-over  are  74  short  and  21  long, 
or  a  total  of  95.  If  the  distance  between  gauge 
lines  is  7  feet  5  inches,  use  the  bill  for  7  feet  6 
inches. 

TABLE  No.  32. 

TIMBER  FOR  CROSS-OVERS. 

LENGTH  OF  LAST  SHORT  PIECE. 


CROSS-TIE. 

DISTANCE  BETWEEN  GAUGE  LINES. 

6ft.  6  in. 

6  ft.  9  in. 

7  ft.  o  in. 

7  ft.  3  in. 

7  ft.  6  in. 

7  ft.  9  in. 

Sft.oin. 

Ft.    In. 
8       0 

Ft.  In. 
II    3 

Ft.  In. 
12    0 

Ft.  In. 
12    3 

Ft.  In. 
12     6 

Ft.  In. 
12    9 

Ft.  In. 
12    O 

Ft.  In. 
13    3 

8       6 

II    3 

II     6 

II    9 

12    O 

12   3 

12    6 

12   9 

LENGTH  OF  LONG  PIECES. 


8   o 
8   6 

19  3 
19  9 

19  6 
20  o 

19  9 
20  3 

20  0 

20  6 

20  3 
20  9 

20  6 
21  0 

20  9 
21  3 

124 


PRACTICAL  SWITCH  WORK. 


TABLE  No.  33. 
NUMBER  OF  LONG  PIECES  IN  No.  6  CROSS-OVER. 


DISTANCE  BETWEEN  GAUGE  LINES. 

CROSS-TIE. 

6ft.  6in. 

6  ft.  9  in. 

7  ft.  o  in. 

7  ft.  3  in. 

7  ft.  6  in. 

7  ft.  9  in. 

8  ft.  o  in. 

Ft.    In. 
8       o 

Feet. 

18 

Feet. 
I? 

Feet. 
16 

Feet. 
15 

Feet. 
H 

Feet. 
13 

Feet. 
12 

8       6 

22 

21 

2O 

19 

is    !    17 

J6 

No. 
18 

7  CROSS-OVE 

17         16 

R. 

I  i 

13 

8       o 

J9 

15 

86         23 

22 

21 

20 

19 

18 

17 

No.  8  CROSS-OVER. 

8      o 

22 

21 

20 

19 

19 

17 

16 

8      6 

25 

24 

23 

22 

21 

20 

19 

No.  9  CROSS-OVER. 


8   o 
8   6 

25 

28 

24 
27 

23 
26 

21 
25 

!9 
24 

17 
23 

16 

22 

No.  10  CROSS-OVER. 


8   o 
8   6 

28 
32 

26 

30 

24 
28 

23 
27 

22 
26 

20 
25 

18 

24 

No.  ii  CROSS-OVER. 


8   o 
8   6 

30 
36 

28 
34 

26 
32 

24 
30 

22 

28 

20 
26 

19 
25 

SWITCH    TIMBER.  12 

TABLE  No.  33  (Continued). 
NUMBER  OF  LONG  PIECES  IN  No.  12  CROSS-OVER. 


DISTANCE  BETWEEN  GAUGE  LINES. 


CROSS-TIE. 

6  ft.  6  in. 

6  ft.  9  in. 

Feet. 
30 

7  ft.  o  in. 

7  ft.  3  in.  7  ft.  6  in. 

7  ft.  9  in. 

Feet. 
24 

8  ft.  oin. 

Feet. 
22 

Ft.    In. 
8       o 

Feet. 
32 

Feet. 
28 

Feet. 
27 

Feet. 
25 

8      6 

39 

37 

35 

32 

30 

28 

26 

No.  15  CROSS-OVER. 


8   o 
8   6 

40 
50 

38 

47 

36 
44 

34 
4i 

32 
38 

30 
-36 

28 
34 

If  the  cross-ties  are  8  feet  long,  the  length  of 
the  long  pieces  is  20  feet  3  inches,  19  of  which, 
instead  of  2 1,  are  necessary.  The  last  short  piece 
being  12  feet  9  inches,  the  number  of  short  pieces 
are  76,  or  a  total  of  95,  the  same  as  for  the  8£ 
feet  cross-tie. 

A  bill  for  any  other  frog  and  distance  between 
gauge  lines  of  parallel  tracks  can  be  obtained  in 
the  same  manner. 

BILL  FOR  THREE-THROW. 
Having  a  bill  of  timber  for  any  single  turnout 
for  any  frog,  it  can  easily  be  converted  into  one 
for  a  corresponding  three-throw  by  subtracting 
one-half  the  length  of  the  8  or  8  feet  6  inch 
cross-tie  from  any  piece  of  timber  in  the  single 


126  PRACTICAL  SWITCH  WORK. 

bill  and  multiplying  the  difference  by  two.  For 
example :  For  a  No.  8  three-throw  the  length  of 
the  pieces  under  the  frog  in  the  single  bill  for  8 
feet  cross-tie  is  12  feet  9  inches;  subtracting  4 
feet,  or  one-half  the  cross-tie,  makes  a  difference 
of  8  feet  9  inches;  twice  8  feet  9  inches  are  17 
feet  6  inches,  or  the  length  of  the  piece  under 
the  frog  in  a  three-throw. 

For  8  feet  6  inch  cross-tie,  the  frog  piece  is 
13  feet  3  inches;  subtracting  4  feet  3  inches,  the 
difference  is  9  feet,  and  multiplying  by  2,  we 
have  1 8  feet  as  the  length  of  the  piece  under  the 
frog  in  a  three-throw. 

The  same  is  true  for  any  other  pieces. 

The  length  of  the  piece  under  the  point  of  the 
crotch  frog  is  the  same  as  that  of  the  piece  under 
the  frog  of  the  single  bill,  which  is  equal  to  the 
gauge  of  the  track  added  to  the  length  of  the 
cross-tie,  or  4  feet  9  inches  and  8  feet  6  inches, 
making  13  feet  3  inches  for  8  feet  6  inch  cross- 
tie,  and  12  feet  9  inches  for  8  feet  cross-tie. 

If  the  three-throw  is  a  stub,  the  single  bill  for 
the  stub  lead  is  to  be  changed,  not  the  bill  for 
the  point  lead. 


The  alignment  of  a  railroad  is  made  up  of 
curves  and  tangents,  tangent  meaning  a  straight 
line.  The  names  of  curves  most  generally  used 
are  Regular,  Compound,  and  Reverse. 

The  flattened  end  of  a  curve  is  known  as 
Elastic,  Parabolic,  Transition,  and  Spiral — all 
being  practically  the  same. 

A  REGULAR  CURVE. 

A  Regular  Curve  is  one  whose  curvature  re- 
mains the  same  as  to  degree  from  beginning  to 


No.  20. 


end.  The  point  where  it  begins  is  denoted  as 
the  P.  C.,  or  point  of  curvature,  and  where  it 
ends  as  the  P.  T.,  or  point  of  tangency. 

This  diagram  represents  a  4- degree  curve;  if 
it  remains  a  4-degree  for  its  entire  length,  A  to 
B,  it  is  a  regular  curve,  because  its  curvature 
neither  increases  nor  diminishes ;  but  if  it  is  for 
a  portion  of  its  length  4  degrees  and  for  the  re- 
mainder changes  one  or  more  times  to  any  other 
degree  than  4,  it  is  a  Compound  Curve. 
(127) 


A  COMPOUND  CURVE. 

A  Compound  Curve  is  made  up  of  a  number 
of  curves  of  different  degrees,  the  number  not 
being  limited,  and  so  connected  as  to  form  a 
continuous  curve,  as  shown  below. 

Its  curvature,  therefore,  increases  or  dimin- 
ishes, but  its  general  direction  remains  the  same. 
In  Diagram  No.  21  it  may  begin,  say  a  4,  then 


No.  21. 

change  to  a  I,  then  to  a  6,  where  it  ends  with 
the  tangent.  It  may  begin  of  any  desirable 
degree  of  curvature  and  be  composed  of  any  de- 
sirable number  of  curves,  every  change  of  which 
is  denoted  at  the  point  where  the  change  begins 
by  P.  C.  C.,  or  point  of  compound  curvature, 
the  beginning  being  denoted  by  P.  C.  and  the 
end  by  P.  T.,  just  as  in  a  regular  curve, 


(128) 


A  REVERSE  CURVE. 

A  Reverse  Curve  is  one  in  which  the  curvature 
reverses,  or  changes  from  one  direction  to  the 
opposite,  from  right  to  left  or  left  to  right,  the 
point  at  which  it  reverses  being  denoted  by  P. 
R.  C.,  or  point  of  reverse  curvature,  as  in  the 
diagram  below. 

The  two  curves  so  reversing  may  be  both  reg- 
ular or  both  compound,  or  one  compound  and 
the  other  regular. 


No.  22. 


The  difference  between  a  compound  and  a  re- 
verse curve  is  this  :  A  compound  changes  as  to 
degree  of  curvature,  and  a  reverse  changes  as  to 
direction.  Two  curves  similar  to  a  reverse,  hav- 
ing a  short  piece  of  tangent  or  straight  line  be- 
tween them,  are  sometimes  erroneously  called  a 
reverse.  Practically,  they  may  be,  but  to  be  a 
genuine  reverse  they  must  reverse  at  a  point 
and  have  no  straight  line  whatever  between 
them.  There  is,  however,  no  objection  to  treat- 
ing a  case  where  there  is  a  short  tangent  prac- 
tically as  a  reverse. 

$  (129) 


THE  DEGREE  OF  CURVATURE. 

The  measure  of  the  curvature,  or  the  sharp- 
ness of  a  curve,  is  called  the  degree  of  curvature. 

As  what  is  meant  by  the  term  "  degree "  is 
beyond  the  clear  understanding  of  any  one  not 
well  advanced  in  mathematics,  no  attempt  will 
be  made  to  explain  it,  beyond  the  idea  that  may 


No.  23. 

be  conveyed  by  explaining  what  is  called  the 
radius. 

THE  RADIUS. 

If  a  string  of  any  convenient  length  be  secured 
at  one  end,  at  the  surface,  of  the  ground,  to  a 
stake,  and,  with  a  sharp  stick  fastened  to  the 
other  end,  a  curve  were  described  upon  the 
ground,  as  shown,  the  string  A  B  would  corre- 
spond to  the  radius. 

(130) 


THE  DEGREE  OF  CURVATURE.  l^\ 

From  the  diagram,  it  is  clear  that  the  shorter 
the  string,  or  radius,  the  sharper  the  curve,  and, 
also,  the  longer  the  string,  or  radius,  the  longer  or 
flatter  the  curve.  To -describe  a  i-degiee  curve, 
the  string  would  have  to  be  5730  feet  long,  and 
a  lo-degree  curve  it  would  be  one-tenth  of  5730 
teet,  or  573  feet.  So,  to  know  what  the  radius 
of  any  curve  is,  divide  5736  by  the  degree  of  the 
curve.  The  correct  radius  is  5729  feet  8  inches, 
but  5730  feet  is  sufficiently  correct  and  is  gener- 
ally used. 

The  reason  the  amount  of  curvature  is  ex- 
pressed as  the  degree  of  curvature,  is  because 
curves  are  laid  out  not  in  the  manner  shown, 
but  by  means  of  a  surveying  instrument  upon 
the  curve  itself,  the  different  points  of  which 
are  located  or  determined  by  means  of  degrees 
which  are  equal  sub-divisions  of  a  circle. 

As  the  trackman's  knowledge  of  curvature  is 
largely  by  comparison  with  other  curves  known 
to  him,  a  knowledge  of  what  the  radius  is  may 
convey  an  idea  as  to  the  degree  or  to  the  extent 
which  one  curve  differs  from  another.  The  fol- 
lowing is  a  table  of  degrees  with  the  correspond- 
ing radius: — 


132 


PRACTICAL  SWITCH  WORK, 


TABLE  No.  34. 
DEGREE  OF  CURVATURE  WITH  CORRESPONDING  RADIUS. 


DEGREE. 

RADIUS.                  DEGREE. 

II 

RADIUS. 

Feet. 

Feet. 

I 

5730 

ii 

521 

2 

2865                      12                      477 

3 

1910                            13                            441 

4 

H33                      14                       409 

5 

1146               15               380 

6 

955 

re                   358 

7 

819 

i7                   338 

8 

717 

18 

318 

9 

637 

19 

301 

10 

573 

20      . 

286 

TO   ASCERTAIN   THE  DEGREE 
OF  CURVATURE. 

As  a  matter  of  information  merely,  every  fore- 
man should  know  the  degree  of  curvature  of 
every  curve  on  his  section,  and,  also,  the  way  to 
ascertain  it.  In  addition  to  this,  he  should  know 
what  it  is,  so  as  to  intelligently  determine  the 
proper  elevation,  the  basis  of  which  is  a  certain 
amount  for  every  degree  of  curvature,  according 
to  the  speed. 

To  ascertain  the  degree  of  any  curve,  take  a 
fine  twine  string  about  64  or  65  feet  long,  and 
about  12  inches  from  either  end  tie  a  knot;  from 
this  knot,  with  the  string  stretched  tight,  meas- 
ure carefully  31  feet  and  tie  another  knot ;  con- 
tinue this  measurement,  and  31  feet  further  tie 
another  knot,  the  distance  between  the  extreme 
knots,  at  A  and  B,  being  62  feet,  the  interme- 
diate knot  being  at  C,  or  exactly  midway  be- 
tween them,  as  shown  in  Diagram  No.  24. 

At  any  point  upon  the  curve,  hold  one  of  the 
knots  at  the  end  upon  the  gauge  side  of  the  rail 
head,  as  at  A,  and,  with  the  string  stretched 
tight,  place  the  knot  at  the  other  end  of  the 
string  upon  a  corresponding  point,  as  B,  at  the 
gauge  side  of  the  rail  also. 
(i33) 


134  PRACTICAL  SIVTTCH  WORK. 

At  the  middle  knot  C,  with  a  foot-rule,  meas- 
ure carefully  the  distance  from  the  string  to  a 
point  on  the  rail  head  corresponding  to  that  at 
which  each  end  of  the  string  is  placed,  and  the 
distance,  in  inches,  from  the  string  to  the  rail  will 
be  equal,  approximately,  to  the  degree  of  curva- 
ture. The  distance  to  the  rail  at  the  middle 
knot  is  called  the  middle  ordinate  of  a  chord, 
and  is  sometimes  known  to  foremen  as  the  "  mid- 
dle distance." 

The  string  corresponds  to  the  chord  and  the 
curving  rails  between  the  ends  of  the  string  cor- 


respond to  the  arc  or  portion  of  a  circle.  Ac- 
cording as  the  string  is  long  or  short  the  middle 
ordinate  is  great  or  small.  In  sharp  curvature 
it  is,  therefore,  greater  than  in  light  curvature. 

The  reason  the  length  'of  the  string  between 
the  extreme  knots  should  be  preferably  62  feet 
is,  that  when  that  length  is  applied  to  a  I -de- 
gree curve  it  will  give  a  middle  ordinate  of  I 
inch,  and  2  inches  for  a  2-degree  curve,  3  inches 
for  a  3-degree  curve,  and  so  on  for  any  curve. 

This  method  of  ascertaining  the  degree  will 
not  give  the  degree  so  accurately  as  it  can  be 


TO  ASCERTAIN  THE  DEGREE  OF  CUR  I/A  TURE.   135 

obtained  by  an  engineer  with  an  instrument, 
but  it  can  be  depended  upon  as  sufficiently  ac- 
curate for  practical  purposes,  such  as  for  elevat- 
ing. 

Because  a  string  62  feet  long  will  give  a  mid- 
dle ordinate  of  i  inch  when  applied  to  a  i-de- 
gree  curve,  it  does  not  follow  that  one  just  half 
as  long,  or  31  feet,  will  give  an  ordinate  of  £ 
inch  if  applied  to  the  same  curve. 

The  length  of  the  string  which  will  give  % 
inch  on  a  i~degree  curve  is  44  feet. 

The  following  table  gives  the  different  lengths 
of  string  and  the  corresponding  ordinate,  when 
applied  to  a  I -degree  curve. 

TABLE  No.  35. 
WHEN  APPLIED  TO  A  ONE-DEGREE  CURVE. 


LENGTH  OF 
STRING. 

> 

MIDDLE  ORDI- 
NATE. 

LENGTH  OF 
STRING. 

MIDDLE  ORDI- 
NATE. 

Feet. 

Inches. 

Feet. 

Inches. 

76 

i^ 

49 

# 

69 

i# 

44 

% 

66 

i# 

39 

y* 

62 

I 

31 

X 

58 

H 

22 

% 

54 

X 

Some  trackmen  have  been  taught,  and  find  it 
very  convenient,  to  use  a  43,  50,  or  54-foot  string 
for  the  same  purpose,  and  it  is  proper  for  them 


136  PRACTICAL  SWITCH  WORK. 

to  continue  to  do  so  if  desirable,  as  the  same  re- 
sult can  be  obtained  with  a  string  of  any  reason- 
able length.  There  is,  however,  an  advantage 
in  using  the  62-foot  length,  as  it  will  give  an  or- 
dinate  of  i  inch  on  a  I -degree  curve,  and  for  any 
curve  greater  than  a  i -degree  the  ordinate  will 
be  as  many  times  greater  than  i  inch  as  the 
curvature  is  more  than  i  degree. 

For  example :  A  62-foot  string  will  give  an 
ordinate  of  3  inches  on  a  3-degree  curve;  6 
inches  on  a  6-degree  curve;  20  inches  on  a  20 
degree  curve,  and  so  on  for  any  number  of  de- 
grees, the  length  of  the  ordinate  always  corre- 
sponding to  the  degree.  So  it  may  be  taken  as 
a  safe  rule  that  in  every  case  where  a  62-foot 
string  is  used  the  middle  ordinate,  in  inches,  cor- 
responds approximately  to  the  degree  of  curva- 
ture. 

By  reference  to  Table  No.  35,  it  is  seen  that 
a  43,  50,  and  54-foot  chord  or  string  gives  \,  f , 
and  f-inch  ordinates,  respectively,  for  i  degree  of 
curvature.  To  ascertain  by  these  lengths  what 
the  curvature  of  any  curve  above  i  degree  is,  it 
is  necessary  to  divide  the  ordinate  by  the  frac- 
tions of  an  inch  corresponding  to  those  lengths 
of  string.  This  is  more  difficult  than  by  using  a 
62-foot  string,  which  will  show  at  a  glance  what 
the  degree  is. 


TO  ASCERTAIN  THE  DEGREE  OF  CURVATLRE.   l^] 

The  ordinate  should  be  measured,  not  at  one 
place  alone,  but  at  several  points,  before  being 
satisfied  as  to  what  the  degree  is,  although  gen- 
erally one  measurement  should  be  sufficient  to 
give  an  idea  of  what  the  curvature  is. 


THE  LIMIT  OF  CURVATURE. 

There  is  a  limit  to  curvature  for  the  economi- 
cal operation  of  a  railroad,  and,  while  for  main 
track  it  is  desirable  not  to  exceed  a  curvature  of 
2  or  3  degrees,  it  may  sometimes  be  necessary  to 
exceed  even  10.  Six  degrees  should  be  the 
maximum  for  main  tracks  of  the  standard  4 
feet  8£  inch  and  4  feet  9  inch  gauges.  However, 
sharp  main-track  curves  are  unavoidable  rather 
than  optional. 

In  main-track,  turnout  curves  as  high  as  17  de- 
grees, which  curve  is  suitable  to  a  No.  6  frog,  are 
a  doubtful  expedient,  it  not  being  advisable  in 
any  case  to  exceed  the  curvature  of  a  No.  8  turn- 
out, or  about  9^-  degrees,  if  it  can  be  avoided. 

The  maximum  curvature  which  can  safely  be 
used  by  a  standard  road  engine,  at  moderate 
speed,  is  about  20  degrees,  and  this  should  be 
the  limit.  Freight  cars  and  yard  or  shifting 
engines,  made  for  sharp  curvature,  can  use  with 
safety  from  40  to  60  degrees,  according  to  their 
construction;  but  these  are  extremes,  to  be 
avoided  as  a  rule. 


(138) 


TO  LINE  A  CURVE. 

Where  the  centre  stakes  of  a  curve  are  given 
by  the  engineer,  it  is  easy  to  line  a  curve  ac- 
curately, but,  generally,  trackmen  have  no  such 
assistance,  and  they  have  to  depend  entirely 
upon  the  eye  for  lining  their  track. 

All  curves,  after  a  few  renewals  of  cross-ties, 
are  more  or  less  out  of  line,  and  have  sharp  and 
flat  places  in  them  which  are  very  noticeable  at 
full  speed.  Such  spots  may  not  be  detected  by 
the  eye  when  lining,  but  they  can  be  by  using  a 
string  and  measuring  the  middle  ordinate  in  the 
same  manner  as  is  done  to  find  the  degree  of 
curvature. 

So  long  as  the  middle  ordinates  are  equal,  or 
nearly  so,  it  indicates  that  the  curvature  is  uni- 
form, but  when  they  vary,  that  is,  increase  and 
decrease  frequently,  it  indicates  very  bad  line, 
and  the  greater  the  difference  between  them,  and 
the  more  frequently  they  change,  the  worse  the 
alignment.  To  correct  such  line,  the  track 
should  be  thrown  at  such  points  so  that,  as  far  as 
possible,  the  ordinates  will  be  nearly  equal.  A 
regular  curve,  whose  ordinates  are  equal,  is  in 
perfect  line,  so  far  as  perfection  in  railroad  work 
can  be  attained. 

(i39) 


I4O  PRACTICAL  SWITCH  WORK. 

To  ascertain  whether  a  curve  is  in  good  line, 
take  a  string  62  feet  long  or  of  any  other  rea- 
sonable length,  and  knot  it  in  the  manner  ex- 
plained on  page  133,  and  measure  the  middle 
ofdinates  and  mark  each  one  with  chalk  upon 
the  base  of  the  rail  at  the  point  where  it  is 
measured,  beginning  at  the  point  of  the  curve 
and  continuing  around  the  curve,  as  shown,  A 
to  C,  B  to  D,  C  to  E,  in  the  diagram  below. 


No.  25. 


If  the  length  of  the  string  or  chord  is  62  feet, 
that  will  be  the  distance  from  A  to  C,  and  so  on. 

From  A  to  B  being  one-half  the  length  of  the 
string,  the  ordinate  will  thus  be  measured  every 
31  feet,  and  by  marking  it  distinctly  upon  the 
base  of  the  rail  with  chalk,  it  can  easily  be  seen 
whether  or  not  the  curve  is  in  good  line.  If  it 
is,  all  the  ordinates  will  be  nearly  equal ;  if  it  is 
not,  they  will  vary,  and  the  greater  the  difference 
the  worse  the  line. 

Write  the  ordinates  upon  a  piece  of  paper  in 
the  order  measured,  so  that  it  can  be  seen  at  a 
glance  what  they  are  for  the  whole  curve. 


TO  LINE  A   CURVE.  141 

Suppose,  starting  from  the  beginning  of  the 
curve,  it  should  be  found  that  they  were  nearly 
uniform,  something  like  as  follows:  4j  inches, 
4j  inches,  3f  inches,  4^  inches,  4^  inches,  4^ 
inches.  It  indicates  that  the  curve  is  in  very 
fair  line,  because  the  ordinates  vary  but  little, 
and,  also,  that  the  curvature  is  about  4^  degrees, 
and  all  that  can  be  done  to  improve  it  would  be 
to  throw  the  track  towards  the  high  side  of  the 
curve  a  little,  to  slightly  increase  the  curvature 
at  the  place  where  the  ordinate  is  3^  inches, 
which  indicates  slightly  decreased  curvature  at 
that  ordinate  point. 

But  if  the  ordinates  vary  something  like 
this:  4j  inches,  6J-  inches,  5|-  inches,  5^  inches, 
4-J  inches,  6f  inches,  4^  inches,  3  inches,  it  indi- 
cates that  the  curve  is  not  in  good  line. 

To  remedy  a  case  where  the  defect  in  the 
alignment  is  so  marked,  the  foreman  must  rely 
upon  his  exercise  of  good  judgment.  Where 
the  ordinates  are  6J-  and  6f  inches,  the  track 
should  be  lined  toward  the  centre,  or  inside,  of 
the  curve,  and  the  lining  carried  in  both  direc- 
tions, reducing  slightly  the  intervening  ordinates 
so  that  they  all  may  be  uniform. 

It  is  not  advisable  to  throw  the  track  toward 
the  high  side  at  the  points  where  the  ordinates 
are  small,  unless  the  difference  between  them 


142  PRACTICAL  SWITCH  WORK. 

and  the  next  change  is  considerable  and  contin- 
ues for  some  distance  around  the  curve.  In 
such  a  case,  the  sharp  places  should  be  lined  to- 
wards the  centre  and  the  flat  ones  towards  the 
high  side  of  the  curve. 

After  the  curve  has  been  thrown  for  the  pur- 
pose of  correcting  the  line,  begin  again  at  the 
starting  point  and  measure  the  ordinates  again 
and  mark  the  length  of  each  upon  the  base  of 
the  rail,  having  rubbed  out  the  chalk  mark  first 
made  at  the  same  point. 

If  the  ordinates  are  found  to  be  equal,  or 
nearly  so,  then  the  curve  should  be  satisfactory. 
tf  not,  then  throw  it  where  it  is  necessary  and 
measure  the  ordinates  again,  and  continue  to 
throw  and  measure  until  it  is  satisfactory.  A 
little  experience  will  enable  the  foreman  to  im- 
prove bad  curves  rapidly  and  intelligently,  al- 
though at  first  the  work  will  be  slow,  and  per- 
haps tedious  and  faulty. 

What  has  just  been  mentioned  refers  to  regu- 
lar curves.  It  may  happen  that  after  going 
some  distance^  around  the  curve  the  ordinates 
suddenly  increase  or  decrease,  and  then  continue 
nearly  uniform  for  the  remainder,  or  for  a  por- 
tion of  the  remainder,  of  the  curve.  For  example  : 
Those  first  measured  may  be  2|  inches,  2f  inches, 
z\  inches,  2\  inches,  2f  inches,  3  inches,  and 


TO  LINE  A   CURVE.  143 

then  change  to  5  inches,  5^  inches,  sj  inches, 
5  inches,  5  inches,  5^  inches.  This  would  indi- 
cate that  the  curve  began  about  2%  degrees  and 
was  then  compounded  at  a  certain  point  to  5 
degrees. 

Wherever  a  change  like  this  occurs,  and  if 
beyond  where  the  change  occurs  the  ordinates 
are  nearly  equal,  it  is  fair  to  presume  that  it  is  a 
compounded  curve.  The  change  from  one  com- 
pound to  another  should  be  made  gradually  so 
as  to  blend,  as  it  were,  from  the  3  to  the  5-degree 
curve,  or  from  the  3  to  the  5-inch  ordinate. 

Between  the  3  and  5-inch  ordinates  there 
would  be  a  sharp  spot,  which  should  not  be  per- 
mitted to  remain,  and  which  should  be  removed 
by  throwing  the  track  towards  the  low  side  until 
the  ordinates  increase  gradually  from  2j  to  5 
inches. 

There  should  be  no  such  abrupt  changes  in  a 
curve,  and,  ordinarily,  any  stakes,  stones  or  mon- 
uments placed  for  the  permanent  marking  of  the 
alignment  of  the  curve  where  the  compounds 
are  so  abrupt,  should  be  disregarded,  if,  by  ad- 
hering to  them,  the  track  could  not  be  made  to 
give  smooth  riding  to  the  train,  as,  after  all,  that 
is  what  is  desired. 

The  points  or  ends  of  curves  thrown  to  a  line 
so  marked  may  not  only  be  objectionable  when 


144  PRACTICAL  SWITCH  WORK. 

in  their  best  condition,  but  are  liable  to  become 
more  so  as  they  become  sharper,  from  gradually 
yielding  to  the  tendency  of  the  train  to  go  to- 
wards the  outside  of  the  curve. 

The  starting  point  for  measuring  the  ordinates 
is  optional  and  may  be  at  either  end  of  the 
curve.  Place  one  end  of  the  string  upon  the 
rail  where  the  curve  begins,  and,  having  measured 
and  marked  the  middle  ordinate  upon  the  rail, 
move  up  and  place  the  same  end  of  the  string 
upon  the  rail  at  the  chalk  mark  and  measure 
the  new  ordinate,  and  thus  proceed  around  the 
curve.  It  will  take  three  men  to  do  this,  one  at 
each  end  of  the  string  and  one  at  the  middle  to 
measure  and  mark  the  ordinates. 

This  method  of  lining  can  be  used  in  all  cases, 
and  particularly  where  the  track  has  been  raised 
or  cross-ties  renewed,  and  it  is  the  desire  to  have 
good  line  without  an  instrument.  It  is  recom- 
mended, also,  to  show  up  any  bad  swings  in 
curves  which  are  not  perceptible  to  the  eye,  and 
particularly  those  at  the  beginning  of  the  curve, 
which  are  caused  by  the  curve  being  too  sharp 
at  that  point. 

One  of  the  reasons  such  "  kinks  "  are  permitted 
to  remain  in  main-track  curves  so  long  is,  that 
foremen,  as  a  rule,  are  averse  to  throwing  the 
track  wherever  it  is  necessary  to  cut  the  rails  to 


TO  LINE  A   CURVE.  145 

do  so.  Sometimes,  also,  being  under  the  impres- 
sion that  their  curves  are  nearly  right,  they  hesi- 
tate to  disturb  them  *T.  uch,  fearing  that  they  may 
be  made  worse  ratftei  trian  better,  or  that  such  a 
re-lining  may  ^ive  tnem  too  much  extra  work. 

This  fear  need  not  exist  so  long  as  the  track 
is  thrown  umtorrn'.y  and  nearly  equal  ordinates 
are  obtained.  Whatever  distance  the  track 
should  be  moved  to  give  it  good  line,  whether 
it  be  one  inch  or  one  foot,  although  it  may  make 
a  little  extra  work,  the  sooner  it  is  so  moved 
the  better,  provided  no  better  reasons  exist  for 
not  doing  so  than  those  just  given. 

On  a  warm  day,  on  account  of  expansion,  it  is 
difficult  to  throw  the  track  towards  the  inside  of 
a  curve,  hence  it  is  the  practice  to  throw  it 
towards  the  high  side  when  re-lining,  and  the 
effect  is  to  be  seen  at  the  ends,  the  curve  being 
outside  of  the  tangent,  and  when  it  is  so,  it  is  the 
endeavor  to  hide  this  defect  in  the  alignment  by 
throwing  out  the  tangent,  and,  as  a  result,  both 
the  curve  and  the  tangent  are  distorted. 

It  is  only  necessary  to  go  some  distance  upon 
the  tangent  to  see  the  effect  of  such  work.  When 
near  the  end,  the  curve  should  be  thrown  in  and 
flattened  and  the  rails  cut,  should  it  be  necessary 
to  do  so,  so  as  in  no  case  to  have  the  end  of  the 
curve  outside  of  the  tangent, 
10 


146  PRACTICAL  SWITCH  WORK. 

It  is,  likewise,  the  practice  to  throw  towards 
the  outside  to  remove  a  sharp  place.  This 
should  not  be  done  so  generally,  as  a  defect  of 
this  kind  can  be  corrected  better  by  throwing 
the  track  toward  the  inside. 

Where  a  point  like  this  cannot  be  remedied 
in  this  manner,  the  rails  should  be  cut  so  that 
the  track  can  be  re-lined  and  remain  where  it  is 
placed  after  re-lining. 

In  lining  by  ordinates,  the  detail  of  the  line 
should  be  gone  over  carefully  and  all  the  little 
kinks  taken  out  before  the  ordinates  are  meas- 
ured the  second  time. 

There  are  other  methods  of  lining  a  curve, 
but  they  are  all  more  or  less  elaborate  or  com- 
plicated, and  depend  very  much  upon  the  sur- 
face of  the  adjacent  land  being  level  and  favor- 
able to  sight  and  measurement. 

What  the  trackman  needs  is  to  know  how  to 
detect  and  remove  sharp  and  flat  places  in  his 
curves,  and  to  change  gradually  from  one  com- 
pound to  another.  All  this  can  be  done  most 
easily  by  the  method  just  given. 

It  is  not  to  be  supposed  that  only  a  62-foot 
string  can  be  used.  One  of  any  reasonable 
length  will  do  just  as  well.  The  reason  one  62 
feet  long  is  recommended  is  that  it  is  a  good 
length,  a  short  one  giving  too  small  an  ordinate 


TO  LINE  A   CURVE. 

for  comparison,  and  because  it  is  that  length  by 
which  the  foreman  can  most  easily  obtain  the 
degree  of  curvature,  and,  consequently,  with 
which  he  is  likely  to  be  most  familiar.  A  string 
of  any  length  between  30  and  100  feet  will  do, 
there  being  no  necessity  for  confining  to  any  par- 
ticular length. 

What  sometimes  appears  to  be  bad  alignment 
in  a  curve  is  due  to  a  depression  in  the  grade  or 
surface  of  the  track  extending  for  several  rail 
lengths.  In  raising  track,  it  is  sometimes  raised 
too  much  and  a  "hump"  is  the  result,  and  in 
running  over  it  to  hide  it,  the  grade  is  not  main- 
tained, and  a  "hole"  in  the  grade  is  the  result, 
which  shows  itself  more  in  the  alignment  than 
in  the  surface.  When  attention  is  called  to  it, 
it  is  invariably  suggested  to  "  throw  the  curve  to 
line"  to  remedy  it.  This  is  wrong — the  depres- 
sion should  first  be  raided. 


THE  ELEVATION  OF  CURVES. 

It  is  the  general  supposition  that  wherever 
there  is  curvature  there  should  also  be  eleva- 
tion; that  the  mere  fact  of  the  existence  of 
curvature  implies  the  necessity  of  a  correspond- 
ing elevation,  but  this  is  erroneous.  Because  a 
curve,  whether  it  is  a  main-track  or  a  siding 
curve,  happens  to  be  of  say  4,  6,  or  any  other 
degree  of  curvature,  it  does  not  follow  that  for 
that  reason  alone  it  should  have  a  corresponding 
amount  of  elevation  in  inches,  or,  it  may  be, 
have  any  elevation  at  all. 

However,  the  rule  so  generally  used  of  a  cer- 
tain amount  of  elevation  for  each  degree  of  curva- 
ture may  be  taken  as  a  safe  guide,  so  long  as  the 
total  amount  does  not  exceed  7  inches ;  but,  as 
elevation  is  for  speed  rather  than  for  curvature, 
any  inflexible  rule  of  I  inch,  ^  inch,  or  any 
other  fraction  of  an  inch  per  degree,  whether  it 
is  more  or  less  than  i  inch,  cannot  always  be 
used  to  advantage  nor  applied  to  various  rates  of 
speed,  degrees  of  curvature,  grades  and  other  gov- 
erning conditions  to  be  met  in  railroad  operation. 

For  example :  On  a  double-track  road,  where 
is  a  grade  of  say  50  to  100  feet  per  mile, 
(J48) 


THE  ELEVATION  OF  CURVES.  149 

the  elevation  of  the  curve  of  the  ascending  track 
should  not  be  as  much  as  that  of  the  descending 
track;  and,  in  case  of  a  curve  upon  a  summit,  the 
amount  of  elevation  should  be  less  than  that  of 
the  same  degree  of  curvature  of  a  comparatively 
level  track. 

On  a  single  track  there  can  be  no  such  pro- 
vision made  for  direction  as  can  be  done  on 
double  track,  and  the  proper  way  is  to  be  gov- 
erned in  elevating  by  the  amount  and  character 
of  the  business  which  predominates,  and  assume 
a  safe  average  rate  of  elevation  for  a  compara- 
tively high  speed,  so  as  to  accommodate  freight 
and  passenger  trains  in  both  directions.  An  ele- 
vation of  f,  -J,  or  i  inch  per  degree  will  do  this, 
it  being  merely  a  matter  of  opinion  as  to  which 
of  these  rates  is  preferable. 

Where  the  traffic  is  almost  exclusively  freight, 
there  being  only  a  few  comparatively  fast  passen- 
ger trains,  there  need  not  be  so  much  elevation 
as  where  the  passenger  business  is  considerable 
and  speed  consequently  greater.  Three-fourths 
of  an  inch  per  degree  is  a  good  elevation  for 
such  conditions. 

But  where  the  freight  and  passenger  business 
are  of  about  equal  importance,  although  the 
passenger  trains  may  attain  a  high  rate  of  speed, 
a  rate  of  elevation  should  be  adopted  which  will 


TJO  PRACTICAL  SWITCH  WORK. 

take  them  at  high  speed,  and,  at  the  same  time, 
retard  as  little  as  possible  the  movement  of  the 
freight  trains  at  a  comparatively  low  speed, 

The  extremes  of  practical  elevation,  therefore, 
are  about  i^  inches  per  degree  for  the  highest 
and  £  inch  per  degree  for  the  lowest.  By  ex- 
perience, it  will  be  found  that  for  heavy  freight 
and  fast  passenger  trains  nothing  less  than  i 
inch  per  degree  should  be  used,  and  that  amount 
is  recommended  so  long  .as  the  total  elevation 
does  not  exceed  6J  or  7  inches,  which  is  as  much 
elevation  as  should  ever  be  put  in  any  curve. 

Unless  the  speed  is  very  low,  J  inch  per  de- 
gree is  rather  too  low  a  rate,  for  the  reason  that, 
although  for  a  short  time  after  a  curve  has  been 
put  up  this  elevation  will  remain,  after  a  while, 
however,  particularly  with  a  poor  quality  of 
ballast  and  poor  road-bed,  the  high  side  of  the 
curve  is  to  be  expected  to  settle,  and  the  small 
amount  of  elevation,  which  at  first  appeared  to 
be  sufficient,  disappears  in  places  and  the  riding 
of  the  curve  is  consequently  very  bad.  A  higher 
rate  of  elevation  would  allow  the  curve  to  settle 
and  yet  better  preserve  the  agreeable  and  safe 
riding  of  the  train  and  the  good  alignment  of  the 
curve. 

High  spots  in  the  low  rail  or  low  spots  in  the 
high  rail  make  very  bad  riding  track,  there  not 


THE  ELEVATION  OF  CURVES.  \^l 

being  a  sufficient  total  elevation  to  counteract 
the  increased  tendency  at  high  speed  to  go 
towards  the  outside  of  the  curve,  and  such 
places  produce  corresponding  defects  in  the 
alignment,  which,  in  turn,  contribute  to  destroy 
the  elevation. 

Three-quarters  of  an  inch  per  degree  is,  there- 
fore, recommended  in  preference  to  -J-  inch  as  a 
minimum  elevation  for  low  speed.  However, 
if  not  much  elevation  is  desired  or  required,  £ 
inch  per  degree,  for  a  speed  of  say  30  miles  per 
hour,  is  very  good. 

Having  a  certain  amount  of  elevation  per 
degree  is  not  so  much  an  object  to  be  attained, 
provided  it  is  not  unreasonably  high  or  low,  as 
the  manner  in  which  the  curve  is  elevated.  The 
quality  of  the  work  of  the  foreman,  therefore, 
enters  as  largely  into  the  consideration  of  this 
question  as  a  precise  amount  of  elevation  per 
degree  of  curvature. 

The  mistake  is  not  infrequently  made  of  as- 
signing either  insufficient  or  excessive  elevation 
as  the  cause  of  a  curve  riding  badly,  when  the 
real  cause  is  more  likely  to  be  from  a  lack  of 
uniformity  in  the  elevation,  for  which  the  fore- 
man alone  is  responsible,  and  which  is  often  not 
thought  of  when  expressing  an  opinion  as  to  the 
reason  a  curve  does  not  ride  well. 


152  PRACTICAL  SWITCH  WORK. 

So  long  as  both  rails,  parallel  and  perfect  as 
to  alignment,  are  put  up  and  maintained  uni- 
formly as  to  elevation,  the  curve  will  ride  well, 
whether  the  elevation  is  ^  or  i  inch  per  degree, 
provided  the  speed  is  not  excessive. 

The  quality  of  the  work  of  the  trackman  is, 
therefore,  of  as  much  importance,  if  not  more, 
than  simply  the  indiscriminate  observing  of  a 
certain  amount  per  degree. 

One  and  a  half  inches  per  degree  is  an  exces- 
sive and  exceptional  elevation  and  should  not 
be  used  in  curves  above  2  or  3  degrees,  because 
that  rate  is  for  a  speed  of  70  or  more  miles  per 
hour,  which,  as  a  rule,  is  impracticable  where  the 
curvature  is  more  than  3  degrees. 

Curves  of  2  degrees  and  less  sometimes  re- 
quire more  elevation  in  proportion  than  sharper 
ones,  as  upon  them  as  high  a  rate  of  speed  can 
be  attained  as  can  be  upon  a  straight  line,  or 
higher  than  that  upon  sharper  curves.  As  much 
as  2  inches  per.  degree  in  a  I  or  2-degree  curve 
may,  perhaps,  be  admissible  for  very  high  speed, 
but  the  conditions  which  require  so  much  must 
be  exceptional  and  not  imaginary. 

A  long,  light  curve  of  say  I  degree  is  difficult 
for  the  trackmen  to  line  accurately,  and  is,  there- 
fore, liable  to  have  in  it  places  where  the  curva- 
ture may  have  been  increased,  in  consequence,  to 


THE  ELEVATION  OF  CURVES.  I  53 

2  or  more  degrees,  which  makes  the  curve  seem 
to  require  a  corresponding  higher  elevation. 
This  is  often  assigned  as  the  reason  more  eleva- 
tion should  be  given  a  curve  than  the  rule  gives  it. 

The  necessity  of  such  an  increase  is  local,  and 
if  the  curve  were  properly  lined  this  necessity 
would  probably  be  removed  and  the  curve  ele- 
vated at  a  less  rate.  To  use  a  rule  of  a  certain 
amount  of  elevation  per  degree  presupposes  that 
the  foreman  knows  what  is  the  degree  of  curva- 
ture of  all  the  curves  on  his  section,  and,  also, 
where  the  points  of  his  compound  curves  are, 
if  he  has  any  curves  of  this  kind. 

As  a  general  thing,  this  information  is  not  pos- 
sessed by  him,  and  if  he  is  not  able  to  obtain  it 
for  himself,  even  approximately,  the  elevating  he 
does  is  liable  to  be  largely  guesswork,  and  par- 
ticularly so  if  any  of  his  curves  are  compounds. 

Before  he  attempts  to  do  any  elevating  what- 
ever he  should  first  ascertain  what  is  the  degree 
of  the  curve  he  intends  to  elevate,  and,  having 
done  that,  then  decide  upon  the  amount  of  ele- 
vation per  degree  which  may  be  considered  nec- 
essary. This  amount  of  elevation  should  de- 
pend upon  the  rate  of  speed,  not  upon  the 
amount  of  curvature.  That  is,  if  it  is  possible  to 
attain  a  speed  of  only  about  30  miles  an  hour, 
the  elevation  should  be  at  the  rate  of  about 


154  PRACTICAL  SWITCH  WORK. 

£  inch  per  degree.  If,  however,  as  much  as  60 
miles' an  hour,  or  more,  is  the  usual  rather  than 
an  unusual  speed,  then  the  elevation  should 
be  at  the  rate  of  not  less  than  i  inch  per  degree. 
The  limits  in  the  amount  of  elevation  should 
be  between  -J  and  i  J  inches,  according  to  the 
conditions  mentioned  on  the  preceding  pages. 

It  is  not  to  be  inferred  that  each  curve  on  a 
section  may  have  a  different  elevation  per  degree. 
A  suitable  rate  of  elevation,  from  •§•  to  i \  inches 
per  degree,  should  be  adopted  for  the  whole  road, 
and  any  variation  from  it  should  be  on  account  of 
grades,  double  track  or  importance  of  the  amount 
or  character  of  traffic,  or  some  other  good  reason. 

Upon  some  single-track  curves  the  fastest 
speed  may  be  only  about  30  miles  an  hour  in 
one  direction,  while  in  the  other  it  may  be  45  or 
50,  or  perhaps  more.  The  proper  elevation  for 
them  would  be  either  f  or  -|  inch  per  degree,  not 
exceeding  a  total  of  6J  inches.  This  would 
take  the  fast  trains  safely  and,  at  the  same  time, 
not  retard  the  slow  ones. 

In  the  following  table  are  given  the  elevations, 
at  different  rates  of  speed,  for  curves  to  12  de- 
grees for  speeds  from  10  to  70  miles  an  hour. 


THE  ELEVATION  OF  CURVES. 

TABLE  No.  36. 


"55 


ELEVATION  FOR  DIFFERENT  SPEEDS  IN  MILES 

DEGREE  OF 

PER  HOUR. 

CURVE. 

70 

60 

55 

50 

40 

30 

20 

10 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

I 

iX 

I 

H 

X 

>6 

X 

O 

O 

2 

2^2 

2 

l/4 

i/4 

IX 

I 

X 

O 

3 

3X 

3 

2% 

2X 

1^ 

iX 

I 

y, 

4 

5 

4 

3* 

3 

2X 

2 

JX 

3/4 

5 

6^ 

5 

3X 

3^6 

2)4 

1X2 

I 

6 

6 

5% 

4>£ 

3X 

3 

2 

*# 

7 

,    . 

6^5 

6/^8 

5X 

4^4 

3^2 

^/£ 

i/4 

8 

-,   , 

6^  ^ 

6 

5 

4 

3 

i% 

94- 

6j^ 

r  5^ 

A\4 

7  IZ 

2 

10 

^l/ 

e 

4 

ii 

6 

2  V 

12 

5 

3 

What  should  be  the  elevation  of  a  4-degree 
curve  for  a  speed  not  exceeding  40  miles  per 
hour  ?  Two  and  one-half  inches,  which  we  find 
under  40  and  opposite  4  degrees.  What  should 
it  be  for  the  same  curve  at  60  miles  an  hour? 
Four  inches.  What  should  it  be  for  an  8-degree 
curve  for  30  miles  an  hour  ?  Four  inches.  What 
for  the  same  curve  at  60  miles  an  hour  ?  Not 
more  than  6£  inches,  because  a  speed  of  60  miles 
an  hour  is  not  practicable  upon  an  8-degree 
curve,  and,  therefore,  it  should  not  have  more 
than  the  maximum  for  any  curve,  or  about  6| 
inches. 


156  PRACTICAL  SWITCH  WORK. 

Another  way  of  ascertaining  what  the  eleva- 
tion of  any  curve  should  be,  according  to  the 
speed,  is,  by  considering  the  middle  ordinate  of 
a  chord  of  varying  length  as  being  equal  to  the 
total  elevation,  the  string  or  chord  being  long  or 
short  as  the  speed  is  high  or  low.  This  ordi- 
nate will  be  equal  to  what  the  elevation  should 
be,  not  exceeding  6%  or  7  inches,  for  any  degree 
of  curvature,  the  string  being  applied  in  exactly 
the  same  manner  as  explained  on  page  133  to 
find  the  degree  of  curvature.  This  -is  a  practi- 
cal and  a  correct  method,  and  does  not  depend 
upon  the  trackman  knowing  anything  in  regard 
to  what  the  degree  of  his  curves  may  be. 

It  is  only  necessary  for  him  to  know  what 
length  of  string  or  chord  will  give  the  ordinate 
corresponding  to  the  proper  amount  of  eleva- 
tion. For  example:  To  elevate  at  the  rate  of 
i  inch  per  degree,  he  should  use  a  string  62  feet 
long ;  for  £  inch  per  degree,  a  string  44  feet  long. 

The  following  is  a  table  of  middle  ordinates 
corresponding  to  the  proper  elevation  of  curves 
to  10  degrees  for  speeds  to  75  miles  per  hour; — 


THE  ELEVATION  OF  CURVES. 


157 


TABLE  No.  37. 
MIDDLE  ORDINATES  FOR  ELEVATING. 


MILES  [LENGTH  ' 

PER    j      OF 

HOUR.  iSTRING.  I 


ELEVATION  FOR  DEGREES  OF  CURVATURE. 


i  Feet. 

20  |   31 
25     38 


30 
40 
50 

55 
60 

70 


44 
49 
53 
58 
62 
66 
69 
76 


In. 


i& 


In. 


In. 


1* 


In. 


6° 


In. 

58 


5X 
6 


7° 


8° 


In. 


In. 


To  use  this  table  and  method  it  is  not  neces- 
sary to  know  the  degree  of  curvature. 

Suppose  it  is  desired  to  elevate  a  I -degree 
curve  at  the  rate  of  %  inch  per  degree.  In  the 
third  column,  under  i  degree,  -J-  inch  is  found  op- 
posite 44  feet ;  44  feet,  therefore,  is  the  length 
of  the  chord  or  string  whose  middle  ordinate  in 
a  i -degree  curve  is  %  inch. 

Apply  the  string  as  directed  on  page  133, 
and  elevate  the  curve  as  much  as  the  ordinate 
measures. 

If  the  curve  is  5  degrees,  at  the  same  rate 
and  curvature  the  ordinate  is  2\  inches  and  the 


I  $8  PRACTICAL  SWITCH  WORK. 

elevation  is  2£  inches.  This  is  found  under  5 
degrees  and  opposite  44  feet. 

Upon  the  basis  of  i  inch  per  degree,  the  length 
of  the  string  is  62  feet ;  the  ordinate  and  eleva- 
tion of  a  5-degree  curve  is,  therefore,  5  inches. 

But  in  case  the  degree  of  the  curve  is  not 
known,  what  is  the  length  of  a  string  which 
would  give  a  suitable  elevation  for  a  speed  of 
60  miles  an  hour?  In  the  second  column,  oppo- 
site a  speed  of  60  miles,  62  feet  is  found  to  be 
the  length  of  the  string  or  cord  which  should  be 
applied  to  the  curve,  without  regard  to  what  its 
degree  of  curvature  may  be,  and  its  middle 
ordinate  measured.  Whatever  this  ordinate  is 
should  be  used  as  the  elevation,  provided  it 
does  not  exceed  6J  or  7  inches. 

For  20  miles  an  hour,  a  string  31  feet  long 
will  give  2  inches  elevation  on  an  8-degree 
curve,  and  one  53  feet  long  will  give  an  elevation 
of  3  inches  on  a  4-degree  curve  for  a  speed  of 
50  miles  an  hour. 

In  every  case  the  middle  ordinate  will  indi- 
cate the  elevation.  Sixty  miles  an  hour  is  not 
an  extraordinary  speed,  and,  if  this  rate  is  ever 
attained,  a  string  not  less  than  62  feet  long 
should  be  used  in  elevating,  but  in  exceeding 
that  length  be  sure  that  the  increased  length  is 
necessary,  and  rarely,  if  ever,  exceed  69  feet, 


THE  ELEVATION  OF  CURVES.  I  $9 

The  string  should  be  stretched  tight  and 
carefully  measured  and  knotted  at  each  end  to 
show  its  length ;  also,  a  large  knot  should  be 
made  exactly  midway  between  the  knot  at  the 
ends,  to  mark  the  middle  point  at  which  the  or- 
dinate  is  to  be  measured.  This  middle  knot 
should  be  made  visible  by  wrapping  or  tying 
with  red  thread  or  yarn.  Apply  the  string  as 
directed,  moving  up  either  its  half  or  whole 
length,  as  may  be  desired,  and  elevate  accord- 
ingly. 

A  word  of  caution  is  necessary  just  here.  As 
it  is  almost  impossible  to  line  a  curve  so  per- 
fectly by  the  eye  that  all  the  ordinates  will  be 
equal,  an  elevation  equal  to  each  ordinate 
should -not  be  used  at  each  point,  unless  they 
are  all  nearly  equal  or  uniform. 

This  mistake  is  sometimes  made,  and,  as  a  re- 
sult, there  is  uniformity  in  neither  line  nor  sur- 
face. An  ordinate  suitable  to  the  elevation  at 
all  the  points  should  be  selected  and  the  curve 
elevated  accordingly. 

All  the  ordinates  of  the  curve  should  first  be 
measured  as  directed,  and  the  curve  lined  again 
and  again  until  it  is  uniform;  then  apply  the 
string,  the  length  to  be  taken  from  Table  No. 
37,  and  make  the  elevation  equal  to  the  ordinates 
which  are  nearest  uniform. 


l6o  PRACTICAL  SWITCH  WORK. 

If  there  is  a  decided  difference  in  the  ordi- 
nates,  there  is  a  lack  of  uniformity  in  the  align- 
ment, and  if  the  sharp  places  cannot  be  taken 
out,  the  elevation  should  gradually  increase  or 
decrease  so  as  to  avoid  an  abrupt  change  in  the 
elevation  at  those  points. 

Before  any  elevating  at  all  is  done,  the  curve 
should  be  carefully  lined  and  made  uniform,  the 
grade  rail  being  in  perfect  surface  and  free  from 
irregularities. 

"  Swings,"  that  is,  sharp  places  in  the  curve, 
without  a  corresponding  elevation,  maybe  easily 
found  by  the  trackmen  by  means  of  the  string, 
and  can  be  taken  out  by  throwing  the  curve 
slightly  in  or  out,  as  may  be  necessary,  until  the 
ordinates  are  more  uniform. 

When  a  curve  rides  badly,  before  doing  any- 
thing to  the  elevation  to  remedy  it,  make  a  test 
of  its  alignment  with  the  string,  and,  when  it 
has  been  corrected,  then  attend  to  the  elevation, 
but  not,  as  a  usual  thing,  before  doing  so,  unless 
it  is  evident  at  once  that  the  cause  is  due  to 
the  elevation  and  not  to  the  alignment. 

Look  out  for  sharp  places  at  the  ends  of 
curves,  where  there  is  insufficient  elevation. 


THE  APPROACH  OF  CURVES. 

The  "Approach,"  "Run-off,"  or  "Easement" 
of  a  curve  are  equivalent  expressions  of  the  man- 
ner of  going  upon  or  off  a  curve.  The  method 
most  generally  used  by  trackmen  is  that  of  car- 
rying the  elevation  of  the  curve  out  upon  the 
tangent  at  the  rate  of  about  -J  inch  to  every 
3O-foot  rail. 

When  this  is  done,  the  inside  rail  of  the  curve 
is  assumed  to  be  the  grade  rail — that  is,  it  is 
assumed  to  conform  to  the  grade  line  of  the 
track,  and  it  is  not  affected  by  the  elevation  of 
the  curve. 

Sometimes  in  elevating,  the  grade  line  is  con- 
sidered as  being  in  the  centre  of  the  track,  and 
the  elevation,  obtained  by  raising  the  outside 
rail  of  the  curve  one-half  the  required  elevation 
and  depressing,  or  what  is  equivalent  to  depress- 
ing, the  inside  rail  the  same  amount. 

Sometimes  the  outside  rail  is  regarded  as  be- 
ing the  grade  rail,  and,  in  that  case,  the  inside 
rail  is  depressed  the  full  amount  of  the  eleva- 
tion. These  last  two  methods  are,  however,  the 
exceptions. 

By  depressing,  it  is  not  meant  that  the  track 
(161) 


l62  PRACTICAL  SWITCH  WORK. 

must  be  dug  down  and  the  solid  road-bed  dis- 
turbed. It  means  that  both  rails  should  be  so 
raised  that  when  the  elevating  is  done  the  grade 
line  will  be  either  the  high  rail  or  the  centre 
of  the  track.  This  may  necessitate  raising  a  part 
of  the  straight  line  at  each  end  of  the  curve  suffi- 
ciently to  change  the  grade  line  to  either  rail  or 
to  the  centre  of  the  track,  as  may  be  desired. 

It  is  assumed,  generally,  that  exactly  at  its  be- 
gining  (P.  C.)  and  ending  (P.  T.)  the  curve 
should  have  its  full  elevation,  the  rail  tangent 
to  the  high  side  of  the  curve  being  raised  grad- 
ually from  the  perfect  level  of  the  tangent  and 
attaining  the  full  elevation  exactly  at  the  begin- 
ning (P.  C.)  of  the  curve. 

The  length  of  the  approach  will,  therefore,  de- 
pend upon  the  amount  of  elevation  for  each  30- 
foot  rail,  the  extremes  of  which  are  generally 
£  inch  as  the  least  and  i  inch-  as  the  greatest. 

In  Table  No.  38  is  given  the  length  of  the 
approach,  in  feet,  for  elevating  at  the  rate  of 
£,  f,  f,  and  i  inch  for  every  3<>foot  rail,  for  ele- 
vations from  i  to  7  inches,  7  inches  being  the 
maximum  practicable  elevation  for  more  than  7 
degrees  curvature. 


THE  APPROACH  OF  CURVES,  163 

TABLE  No.  38. 


LENGTH  OF  APPROACH. 

ELEVATION 

OK  CURVE. 

%  Inch. 

y*  Inch. 

Y±  Inch. 

i  Inch. 

Inches. 

Feet. 

Feet. 

Feet. 

Feet. 

I 

60 

48 

4° 

30 

2 

120 

96 

80 

60 

3 

1  80 

144 

120 

90 

4 

240 

192 

160 

1  2O 

5 

300                      240 

200 

150 

6 

360                      288 

240 

180 

7 

420                      336 

280 

2IO 

In  explanation  of  this  table :  What  would  be 
the  length  of  the  elevation  of  the  straight  line 
or  the  approach  of  a  curve  having  4  inches  ele- 
vation and  rising  f  inch  for  each  3O-foot  rail? 

In  the  table  the  answer  is  found  to  be  160 
feet,  or  about  5  rail  lengths.  Measure  this  dis- 
tance from  the  point  of  the  curve,  and,  beginning 
with  a  perfect  level,  raise  the  rail  which  is  tan- 
gent to  the  high  side  of  the  curve,  at  the  rate  of 
£  inch  per  3<>foot  rail. 

In  160  feet,  or  about  5  rail  lengths,  the  full 
elevation  of  4  inches  should  be  attained. 

If  the  outside,  instead  of  the  inside,  rail  is  as- 
sumed to  be  the  grade  rail,  the  approach  will  be 
the  same,  both  as  to  length  and  elevation  per 
rail  length,  just  as  if  the  low  rail  was  the  grade 
rail. 


164  PRACTICAL  SWITCH  WORK. 

If  the  grade  line  is  in  the  centre  of  the  track, 
the  approach  will  be  the  same  as  to  length,  but 
the  high  rail  will  be  raised  and  the  low  rail  de- 
pressed one-half  of  f  of  an  inch,  or  three-eighths 
of  an  inch,  for  every  3<>foot  rail. 

The  same  is  true  of  any  other  elevation  per 
rail  length.  Whether  the  approach  should  be 
long  or  short  is  a  matter  of  opinion,  there  being 
advocates  of  both  ways ;  but,  from  experience,  it 
is  found  that  a  long  and  very  gradual  approach 
of  say  \  inch  per  3O-foot  rail  is  undesirable,  on 
account  of  the  difficulty  to  keep  it  in  proper 
surface,  as  well,  also,  because  it  does  not  always 
impart  the  most  agreeable  motion  to  the  train, 
the  length  of  time  the  car  is  out  of  level  being 
considerable. 

Upon  the  other  hand,  a  short  approach  of  i 
inch  per  3O-foot  rail  is  objectionable  on  account 
of  its  tendency  to  abruptness.  So,  to  avoid 
either  extremes,  f  or  £  inch  is  rather  to  be  pre- 
ferred. 

But,  although  the  practice  of  beginning  the 
elevation  upon  the  straight  line  does  very  well, 
it  is  not  the  best  way  of  going  upon  a  curve, 
and  particularly  so  in  the  case  of  curves  of  4 
degrees  and  more. 

The  true  principle  of  the  approach  is  rather, 
that  wherever  there  is  elevation  there  should 


THE  APPROACH  OF  CURVES.  l6j 

likewise  be  curvature;  and,  although  it  is  in- 
tended by  raising  the  tangent  to  the  full  ele- 
vation at  the  beginning  of  the  curve,  to  enable 
the  train  to  more  easily  change  its  direction 
from  the  straight  line  to  the  curved,  it  only 
partially  accomplishes  what  is  desired,  and  the 
objectionable  lurch  is  not  obviated,  but  is  still 
more  evident  as  the  curvature  increases. 

In  carrying  out  this  idea  of  curvature  where 
there  is  elevation,  the  correct  approach  is  ob- 
tained by  curving  the  tangent  and  flattening  the 
end  of  the  curve  slightly  in  such  a  manner  that 
the  change  from  the  tangent  to  the  curve  is 
made  gradually,  the  curvature  beginning  light, 
say  i  degree  for  about  the  first  50  feet,  2 
degrees  for  the  second  50  feet,  and  3  degrees 
for  the  third  50  feet,  and  so  on,  the  elevation 
also  increasing  correspondingly  to  the  curvature. 
This  makes  the  approach  a  series  of  short  com- 
pounded curves,  and,  practically,  is  equivalent  to 
what  is  called  a  transition  curve,  that  is,  one 
having  a  rapidly  changing  radius  or  increasing 
curvature  for  a  short  distance  between  the  tan- 
gent and  the  full  degree  of  the  curve. 

The  line  of  this  compounded  approach  is  dif- 
ficult to  obtain  without  the  use  of  an  instru- 
ment, but  only  partial  success,  practically,  upon 
the  part  of  the  trackman,  by  his  eye  and  by 


T66  PRACTICAL  SWTTCH  WORK. 

using  the  string  for  the  middle  ordinate,  wili 
give  a  better  approach  in  the  case  of  sharp  curva- 
ture than  that  obtained  by  simply  elevating  the 
tangent. 

If  all  curves  at  the  ends  were  in  correct  align- 
ment, it  would  not  be  difficult  to  give  offset  dis- 
tances, at  points  about  50  feet  apart,  to  which  the 
end  of  the  curve  could  be  thrown  to  make  this 
gradually  increasing  approach,  but,  as  they  are 
invariably  more  or  less  out  of  line,  it  is  impossible 
to  give  anything  which  would  not  be  subject  to 
the  peculiar  conditions  of  each  individual  curve, 
and,  therefore,  could  not  be  reliable. 

There  are  what  are  known  as  spiral  curves, 
easement  curves,  elastic  curves,  &c.,  all  of  them 
being  modifications  of  the  end  of  the  curve, 
equivalent  to  this  curved  approach,  but  they  are 
all  more  or  less  complicated  theoretically,  expen- 
sive, difficult  to  maintain  and  require  an  engi- 
neer with  an  instrument  to  give  their  line,  so 
that,  from  a  practical  point  of  view,  they  are  of 
little  use  to  the  trackman. 

All  that  is  necessary  to  improve  the  approach 
of  any  curve  ought  to  be  so  simple  that  it  can 
be  done  by  the  foreman  himself. 

The  use  of  the  string,  which  is  recommended 
for  lining  and  elevating,  is  also  recommended 
to  assist  the  trackman  in  obtaining  the  line  and 


THE  APPROACH  Of  CURVES.  1 67 

elevation  of  the  approach,  and  should  be  used 
in  the  same  manner. 

As  a  rule,  the  ends  of  curves  are  much  out  of 
line,  it  not  being  rare  to  find  a  4-degree  curve 
increased  to  6  or  7  degrees  at  the  ends. 

This  is  the  accumulating  result  of  the  bad 
practice  of  always  moving  the  track  towards  the 
high  side  and  continuing  the  lining  out  upon  the 
tangent  for  a  short  distance.  The  ends  of  curves 
are  thus  made  too  sharp  and  the  tangent  is  like- 
wise distorted.  This  is  apparent,  not  by  stand- 
ing upon  the  end  of  the  curve  and  looking  in 
the  direction  of  the  tangent,  but  by  standing 
upon  the  tangent  as  far  as  possible  from  the 
curve  and  looking  towards  the  curve.  Where 
this  is  the  case,  it  should  be  corrected  at  once. 

Although  such  defects  in  the  alignment  may 
be  known  to  the  foreman,  they  are  often  long 
permitted  to  remain  because  he  does  not  wish 
to  cut  the  rails  to  correct  them,  which,  gen- 
erally, has  to  be  done. 

But,  as  a  general  thing,  he  is  not  aware  of  the 
real  cause  of  the  curve  being  bad,  and  endeavors 
by  going  over  or  changing  the  elevation  to  rem- 
edy it. 

Whenever  there  is  a  lurch  or  bad  swing  at  the 
beginning  or  end  of  a  curve,  the  first  thing  to  be 
done  should  be  to  measure  the  ordinates  and 


l68  .        PRACTICAL  SWITCH  WORK. 

see  if  the  curve  is  in  correct  line  at  the  ends. 
If  the  ordinates  at  the  ends  are  greater  than 
those  further  around  the  curve,  it  indicates  that 
the  curve  is  sharper  there  than  it  should  be,  and 
the  track  should  be  thrown  towards  the  low- 
side,  cutting  the  rails,  if  necessary;  and  not  only 
should  it  be  thrown  until  the  original,  or  cor- 
rect, curvature  is  restored,  but  it  should  be  flat- 
tened still  more  and  the  change  made  gradually 
from  the  straight  line  to  the  curve  by  means  of  a 
gradually  increasing  curve.  It  will  be  necessary 
to  go  back  upon  the  tangent  from  50  to  100  feet, 
according  to  the  degree  of  the  curve,  to  do  this. 

Wherever  the  end  of  the  curve  appears  to  be 
sharp,  or  outside  of  the  line  of  the  tangent,  it 
will  invariably  be  found  to  be  so,  and  it  should 
at  once  be  corrected,  going  to  considerable 
trouble,  if  necessary,  to  do  it. 

When  the  flattening  is  done,  the  curved  ap- 
proach should  be  elevated  an  amount  corre- 
sponding to  the  increasing  curvature,  rising  grad- 
ually from  the  level  of  the  tangent  to  the  full 
elevation  of  the  curve,  just  as  the  alignment 
gradually  changes  from  a  straight  line  to  the 
full  curvature  in  a  certain  number  of  feet 

The  natural  inquiry  is,  how  much  should  the 
curve  be  thrown  at  the  end  to  make  this  grad- 
ually increasing  approach  ? 


THE  APPROACH  OF  CURVES.  169 

It  is  possible  to  give  this  only  approximately, 
as  it  will  depend  upon  how  much  the  curve  is 
out  of  line  at  the  end  and  also  upon  finding  the 
exact  beginning  or  end  of  the  curve,  and  any 
distances  or  offsets  given  could  be  used  only 
when  the  curve  is  in  correct  alignment ;  so, 
whatever  is  accomplished  will  have  to  be  done 
by  the  trackman  in  his  own  practical  way. 
But  for  the  purpose  of  assisting  him,  in  Table 
No.  39  are  given  some  approximate  distances, 
which  may  be  used  as  offsets  to  be  measured 
from  either  rail  towards  the  inside  of  the  curve, 
to  show  to  about  what  extent  the  end  of  the 
curve  should  be  moved,  provided  it  is  already 
in  good  alignment.  But  as  curves  are  invaria- 
bly out  of  line,  not  too  much  dependence  should 
be  placed  upon  the  figures  in  this  table,  as  they 
are  only  intended  for  curves  already  in  true  align- 
ment, and  also  where  the  ends  (P.  C.  and  P.  T.) 
are  marked  or  when  they  are  correctly  assumed. 

No  curve  or  flattened  approach  is  necessary 
unless  the  curvature  is  4  degrees  or  more. 
Whenever  a  3-degree  curve,  or  less,  seems  to  re- 
quire an  elasticated,  or  flattened,  approach  it  is 
evident  that  the  ends  are  badly  out  of  line,  and 
if  thrown  to  their  correct  line  and  elevated  in  the 
usual  way,  and  kept  in  that  condition,  the  curve 
has  all  that  is  necessary,  provided,  of  course,  the 


170 


PRACTICAL  SWITCH   WORK. 


work  of  the  trackman  is  carefully  done.  In  other 
words,  regular  or  compound  curves  to  3  degrees 
require  no  flattening. 

The  following  is  a  table  of  approximate  off- 
set distances  which  may  be  used  for  lining  ap- 
proaches : — 

TABLE  No.  39. 


OFFSETS  AT  50  FEET  POINTS  ON  CURVE. 

DEGREE. 

IOO 

Feet. 

Feet. 

P.C. 
o. 

50        loo 
Feet.   Feet. 

150 

Feet. 

200 
Feet. 

250 

Feet. 

300 

Feet. 

350 

Feet 

i 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

In. 

4 

.    . 

I 

I/^ 

I 

.    . 

.     . 

.    . 

A.  ^/> 

I 

2 

2 

5 

•  x> 

2 

$ 

6 

I 

.y 

A1/ 

-7  I/ 

2»/ 

3« 

*>l/2 

6 

Sjl 

4 

2^ 

7 

yz 

2 

4X2 

6 

7 

6 

5 

3^2 

iYt> 

i 

2 

5 

lY* 

8 

6 

4/4 

3 

8 

i 

3 

9 

101/2 

10 

8^ 

61/2 

4^ 

2 

To  use  this  table,  assume,  as  nearly  as  possi- 
ble, where  the  curve  begins,  and  mark  this  point 
as  the  beginning  (P.  C),  and  measure  5o-foot 
distances  around  the  curve  as  far  as  may  be  nec- 
essary, making  a  chalk  mark  upon  the  base  of 
the  rail  at  each  5ofoot  point.  Return  to  the 
beginning  (P.  C.)  and  measure  in  the  direction 
of  the  straight  line  50  or  100  feet,  according  to 
the  degree  of  curvature. 


THE  APPROACH  Of  CURVES.  \*]\ 

Measure  the  offset  distance  at  each  point,  taken 
from  the  table,  from  the  inside  base  of  the  rail 
to  the  top  of  a  stake  previously  driven  into  the 
ballast,  level  with  the  top  of  the  cross-tie,  and 
mark  it  upon  the  top.  Throw  the  track  so 
that  the  edge  of  the  base  of  the  rail  is  exactly 
over  the  mark  in  the  top  of  the  stake  and  line  be- 
tween the  points,  and  the  approach,  if  not  exactly 
right,  should  be  something  near  what  is  desired, 
provided  the  end  of  the  curve  was  in  its  true  or 
good  alignment  before  flattened  in  this  manner. 

One  of  the  objections  to  flattening  the  ends 
of  a  curve  is,  that  the  foreman  is  liable  to  make 
the  approach  too  flat,  and,  as  a  result,  increase 
the  curvature  too  much  where  it  joins  the  full 
degree  of  the  curve. 

There  is  a  natural  slight  increase  in  the  curva- 
ture where  the  approach  blends  into  or  is  lost  in 
the  full  curvature,  which  is  of  no  consequence 
practically,  but  if  it  is  still  more  increased  by 
the  beginning  of  the  approach  being  too  flat,  it 
becomes  very  objectionable,  and  what  has  been 
gained  at  the  beginning  of  the  curve  is  thus 
lost  further  upon  it. 

If  the  curve  cannot  be  flattened  enough  by- 
using  the  offsets  in  Table  No.  39,  it  will  likely 
be  found  that  it  is  because  it  is  already  too 
sharp  at  the  end. 


TO  LINE  AND  ELEVATE  A  REVERSE 
CURVE. 

Very  often  what  is  supposed  to  be  a  reverse 
curve  is  not  a  true  reverse  curve  at  all.  As  ex- 
plained on  page  129,  a  reverse  curve  reverses  at 
a  point,  there  being  no  straight  line  whatever 
between  the  curves  forming  it.  However,  any 
two  curves  in  opposite  directions,  having  be- 
tween them  a  short  tangent  of  about  50  or  100 
feet,  do  form  what  is  practically  a  reverse  curve, 
and  may  be  treated  as  such  in  lining  and  ele- 
vating. 

Such  a  piece  of  straight  line  enables  the  re- 
verse to  be  lined  and  elevated  more  easily  than 
if  it  were  a  genuine  reverse,  which,  to  be  im- 
proved easily,  should  have,  where  the  reversing 
point  is  supposed  to  be,  not  a  straight  line,  but 
a  flattening  of  both  curves  slightly  from  the  re- 
versing point,  so  as  to  make  the  curvature  in- 
crease gradually,  as  is  done  in  the  approach  of  a 
curve. 

In  every  case  of  lining  a  genuine,  or  what  may 

be  practically  a  reverse  curve,  the  track  should 

always  be  thrown  or  lined  towards  the  inside  of 

the  curve,  making  the  end  of  the  curve  upon 

(172) 


TO  LINE  AND  ELEVA  TE  A  REVERSE  CURVE.    I  73 

each  side  of  the  reversing  point  similar  to  the 
approach  of  a  curve. 

No  practical  or  reliable  method  can  be  given 
for  accomplishing  this  perfectly ;  it  will  have  to 
be  done  by  the  eye  and  the  exercise  of  good 
judgment  by  the  foreman. 

When  the  reverse  has  been  flattened  after  the 
manner  of  the  approach,  and  appears  to  be  satis- 
factory, then  measure  the  middle  ordinates,  and 
if  they  increase  with  any  degree  of  regularity  it 
is  fair  to  presume  that  the  end  of  the  curve  is 
in  fairly  good  line. 

The  only  difference  between  lining  the  ap- 
proach of  a  regular  curve  and  that  of  a  reverse 
curve  is,  that  in  the  former  the  curvature  can 
be  begun  a  reasonable  distance  out  upon  the 
tangent,  whereas  in  the  latter,  particularly  if  it 
is  a  genuine  reverse,  the  end  of  the  curve  must 
be  flattened  within  itself.  The  result  is,  of 
course,  a  slight  increase,  theoretically,  in  the 
curvature  further  upon  the  curve,  but  it  does  not 
amount  to  much  practically,  and  can  be  dis- 
tributed in  lining  so  as  not  to  affect  the  riding 
of  the  train. 

The  elevating  of  a  reverse  curve  is  done  ex- 
actly in  the  same  manner  as  the  approach  of  a 
curve  is  elevated,  viz.,  by  using  the  middle 
ordinate  of  a  string  or  chord. 


PRACTICAL  SWITCH  WORK. 

The  middle  ordinates  should  be  measured,  and 
a  corresponding  amount  of  elevation  used,  pro- 
vided the  ordinates  increase  regularly  from  noth- 
ing to  the  full  curvature,  just  as  in  an  ordinary 
approach  the-elevation  increases  correspondingly 
with  the  curvature,  that  is,  from  nothing  to  the 
full  elevation. 

At  a  point  midway  between  the  two  curves, 
whether  it  is  the  point  of  reverse  curvature  or  the 
middle  of  a  short  straight  line,  both  rails  should 
be  made  perfectly  level.  If  the  total  elevation 
of  the  curve  is,  say  4  inches,  then  from  this  level 
point  to  where  the  full  elevation  is  reached,  the 
elevation  should  increase  to  4  inches,  at  the  same 
rate  and  in  the  same  distance  that  the  curvature 
increases  from  nothing  to  the  full  curvature, 
whatever  it  may  be. 


The  Trackman's  Helper. 

Revised  Edition.     Price  $1.50,  Prepaid. 

What  Trackmen  Say  of  The  Trackman's  Helper. 

Louisville,  Evansville  and  St.  Louis  Consolidated  Railroad. 

Editor  Roadmaster  and  Foreman — Your  Trackman's 
Helper  has  been  recommended  to  our  roadmasters.  I 
can  simply  say  to  you  that  it  is  a  good  thing  and  should 
be  in  every  roadmaster's  hands,  also  his  trackmen.  Of 
course,  there  are  some  things  about  it  that  an  engineer 
would  criticise,  as  I  do,  but  that  does  not  make  any  dif- 
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You  have  simplified  the  matter  for  trackmen,  and  that  is 
what  is  best  to  be  done.  Yours  truly,  T.  A.  ALLEN. 

The  Missouri  Pacific  Railway  Company. 

Editor  Roadmaster  and  Foreman — I  like  the  Track- 
man's Helper  very  much,  and  I  think  it  is  the  best  book 
of  the  kind  ever  published.  The  book  is  rightly  named. 
I  consider  it  of  great  value  to  trackmen.  I  am  well 
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Chicago  and  Northwestern  Railway  Company. 

Editor  Roadmaster  and  Foreman — I  received  the 
Trackman's  Helper  and  have  perused  its  pages  thorough- 
ly, and  can  say  it  fills  a  long-felt  want  among  our  young 
foremen  and  also  section  men.  While  us  older  men  have 
learned  by  long  experience  and  hard  work  how  to  keep  a 
railroad  in  good  condition  at  a  nominal  cost,  without  any 
help  in  the  way  of  literature,  such  as  your  paper  and 
Trackman's  Helper  give,*  I  have  recommenced  these 
publications  to  all  my  foremen,  as  I  consider  them  the 
best  papers  and  book  published.  F.  W.  SPENCER. 

Wisconsin  Central  Railway. 

Editor  Roadmaster  and  Foreman — I  have  received 
the  Trackman's  Helper.  It  is  a  practical  book.  I  can 
say  it  meets  with  my  approval.  Every  trackman  should 
have  one.  Yours  truly,  F.  C.  BAKER,  R.  M. 


Address  ROADMASTER  AND  FOREMAN,  Pubs., 

91  and  93  S.  Jefferson  St.,  Chicago,  III. 


The  Roadmaster  and  Foreman 

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